SSAT Middle Level Quiz: Interpreting Ratios

20 questions · exam conditions

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Interpreting RatiosQuestion 1 of 20

A cake uses 25 cups flour and 35 cups sugar; simplify flour:sugar ratio.

5:7

7:5

25:35

6:8

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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Interpreting Ratios

Practice Interpreting Ratios in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Interpreting Ratios, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A cake uses 25 cups flour and 35 cups sugar; simplify flour:sugar ratio.

5:7 (correct answer)
7:5
25:35
6:8

Explanation: This question tests SSAT Middle Level skills: interpreting and simplifying ratios. A ratio represents a relationship between two quantities, showing how many times one value contains or is contained within the other. In this scenario, the specific quantities given are 25 cups of flour and 35 cups of sugar and students need to simplify the ratio by finding the greatest common divisor. Choice A is correct because it accurately simplifies the ratio 25:35 to 5:7, demonstrating an understanding of the relationship. Choice B is incorrect because it reflects a common error of reversing the order, which happens when students mix up the items. To help students, encourage them to always check their work by verifying that both parts of the ratio can no longer be divided by the same number. Emphasize the importance of understanding the context of the ratio to avoid reversing quantities.

Question 2

A recipe uses 22 cups flour and 33 cups sugar; simplify flour:sugar ratio.

2:3 (correct answer)
3:2
22:33
4:7

Explanation: This question tests SSAT Middle Level skills: interpreting and simplifying ratios. A ratio represents a relationship between two quantities, showing how many times one value contains or is contained within the other. In this scenario, the specific quantities given are 22 cups of flour and 33 cups of sugar and students need to simplify the ratio by finding the greatest common divisor. Choice A is correct because it accurately simplifies the ratio 22:33 to 2:3, demonstrating an understanding of the relationship. Choice B is incorrect because it reflects a common error of reversing the order, which happens when students switch the sequence. To help students, encourage them to always check their work by verifying that both parts of the ratio can no longer be divided by the same number. Emphasize the importance of understanding the context of the ratio to avoid reversing quantities.

Question 3

A recipe uses 32 cups rice and 40 cups beans; simplify rice:beans ratio.

8:10
4:5 (correct answer)
5:4
32:40

Explanation: This question tests SSAT Middle Level skills: interpreting and simplifying ratios. A ratio represents a relationship between two quantities, showing how many times one value contains or is contained within the other. In this scenario, the specific quantities given are 32 cups of rice and 40 cups of beans and students need to simplify the ratio by finding the greatest common divisor. Choice B is correct because it accurately simplifies the ratio 32:40 to 4:5, demonstrating an understanding of the relationship. Choice A is incorrect because it reflects a common error of not simplifying fully, which happens when students stop after partial division. To help students, encourage them to always check their work by verifying that both parts of the ratio can no longer be divided by the same number. Emphasize the importance of understanding the context of the ratio to avoid reversing quantities.

Question 4

A recipe calls for flour and sugar in the ratio $3:5$ . If Maria uses $12$ cups of flour, how many cups of sugar should she use?

$15$ cups
$20$ cups (correct answer)
$18$ cups
$7.2$ cups
$9.6$ cups

Explanation: When you encounter ratio problems, you're working with proportional relationships between quantities. The key is recognizing that ratios tell you how parts relate to each other, and this relationship stays constant even when the actual amounts change. The recipe calls for flour and sugar in a

3:5

ratio, meaning for every 3 parts flour, you need 5 parts sugar. Since Maria uses 12 cups of flour, you need to find how much this amount has been scaled up from the original ratio. Divide 12 by 3 to get the scaling factor:

12 \div 3 = 4

. This means the recipe has been multiplied by 4. Therefore, the sugar amount must also be multiplied by 4:

5 \times 4 = 20

cups. You can verify this using a proportion:

\frac{3}{5} = \frac{12}{x}

. Cross-multiplying gives

3x = 60

, so

x = 20

. Choice A (15 cups) represents adding 12 + 3 instead of using the scaling factor—a common arithmetic error. Choice C (18 cups) might come from incorrectly thinking the ratio is

2:3

instead of

3:5

, then scaling up. Choice D (7.2 cups) results from flipping the ratio and calculating

\frac{3}{5} \times 12

, which gives you less sugar than flour—impossible when the ratio calls for more sugar. The correct answer is B (20 cups). Strategy tip: In ratio problems, always identify the scaling factor by dividing the given quantity by its corresponding ratio number, then apply that same factor to find the unknown quantity.

Question 5

A paint mixture contains red, white, and blue paint in the ratio $2:3:4$ . If the mixture contains $27$ gallons total, how many gallons of white paint are in the mixture?

$9$ gallons of white paint (correct answer)
$12$ gallons of white paint
$6$ gallons of white paint
$8$ gallons of white paint
$15$ gallons of white paint

Explanation: When you encounter ratio problems, you're working with proportional relationships between different parts of a whole. The key is understanding that ratios tell you the relative amounts, not the actual amounts. The ratio

2:3:4

means that for every 2 parts red paint, there are 3 parts white paint and 4 parts blue paint. To find the actual amounts, first calculate the total number of parts:

2 + 3 + 4 = 9

parts total. Since the mixture contains 27 gallons total, each "part" represents

27 ÷ 9 = 3

gallons. Therefore, white paint makes up

3 × 3 = 9

gallons of the mixture. Looking at the wrong answers: Choice B (12 gallons) would mean white paint represents 4 parts instead of 3 parts—this confuses white paint with blue paint in the ratio. Choice C (6 gallons) suggests each part equals 2 gallons, which would make the total mixture only 18 gallons instead of 27. Choice D (8 gallons) doesn't correspond to any logical calculation from this ratio. The correct answer is A: 9 gallons of white paint. For ratio problems on the SSAT, always follow this three-step process: find the total number of parts in the ratio, divide the actual total by this number to get the value of one part, then multiply by the specific part you need. This systematic approach prevents mixing up which part of the ratio corresponds to which quantity.

Question 6

A school has boys and girls in the ratio $5:7$ . If there are $84$ more girls than boys, how many students are in the school total?

$504$ students in total (correct answer)
$420$ students in total
$336$ students in total
$252$ students in total
$588$ students in total

Explanation: When you encounter ratio problems with a given difference between quantities, you need to use the ratio to find how many "parts" represent that difference, then scale up to find the actual numbers. Given the ratio of boys to girls is

5:7

, this means for every 5 boys, there are 7 girls. The difference between these ratio parts is

7 - 5 = 2

parts. Since there are actually 84 more girls than boys, these 2 parts equal 84 students. Therefore, each part represents

84 ÷ 2 = 42

students. Now you can find the actual numbers: boys =

5 × 42 = 210

students, and girls =

7 × 42 = 294

students. Check:

294 - 210 = 84

✓. The total is

210 + 294 = 504

students. Choice A (504 students) is correct. Choice B (420 students) likely comes from incorrectly thinking each part equals 60 students (

5 × 60 + 7 × 60 = 420

), but this ignores the constraint about the 84-student difference. Choice C (336 students) might result from using 28 students per part instead of 42. Choice D (252 students) could come from using 21 students per part, perhaps from incorrectly dividing 84 by 4 instead of 2. Remember: in ratio problems with given differences, first find how many ratio parts equal the given difference, then determine what each part represents in real units. This method works for any ratio problem with absolute differences.

Question 7

The sides of a triangle are in the ratio $4:5:6$ . If the shortest side is $12$ inches, what is the perimeter of the triangle?

$45$ inches around (correct answer)
$36$ inches around
$30$ inches around
$54$ inches around
$60$ inches around

Explanation: When you see a triangle with sides in a given ratio, you're working with proportional relationships. The key is to find the scale factor that connects the ratio to the actual measurements. The sides are in the ratio

4:5:6

, meaning if we multiply each part by the same number, we get the actual side lengths. Since the shortest side corresponds to the "4" in the ratio and equals 12 inches, we can find this multiplier:

4x = 12

, so

x = 3

. Now we can find all three sides:

4 \times 3 = 12

inches,

5 \times 3 = 15

inches, and

6 \times 3 = 18

inches. The perimeter is

12 + 15 + 18 = 45

inches, which is answer choice A. Looking at the wrong answers: Choice B (36 inches) might result from incorrectly thinking the scale factor is 2 instead of 3, giving sides of 8, 10, and 18 inches. Choice C (30 inches) could come from mistakenly using a scale factor of 2 but then miscalculating the sum. Choice D (54 inches) might occur if you incorrectly identified which part of the ratio corresponds to the shortest side, perhaps thinking the 6 represents the shortest side. Remember: when working with ratios, always identify which part of the ratio corresponds to the given measurement, then use that to find your scale factor. Double-check by verifying that your calculated shortest side matches the given information before finding the perimeter.

Question 8

Three numbers are in the ratio $4:7:9$ . If the largest number exceeds the smallest by $35$ , what is the middle number?

$49$ (correct answer)
$28$
$35$
$42$
$63$

Explanation: When you see numbers given in a ratio, think of them as parts of a whole that can be scaled up or down by the same factor. The key insight is that ratios tell you the relative sizes, not the actual values. Since the three numbers are in the ratio

4:7:9

, you can write them as

4x

7x

, and

9x

for some unknown value

x

. The largest number is

9x

and the smallest is

4x

. Since the largest exceeds the smallest by

35

, you can set up the equation:

9x - 4x = 35

, which simplifies to

5x = 35

. Solving gives you

x = 7

. Now you can find the actual numbers: the smallest is

4x = 4(7) = 28

, the middle is

7x = 7(7) = 49

, and the largest is

9x = 9(7) = 63

. The middle number is

49

, making A correct. Looking at the wrong answers: B)

28

is actually the smallest number in the ratio, not the middle one. C)

35

is the difference between the largest and smallest numbers, which might tempt you if you misread the question. D)

42

doesn't correspond to any meaningful value in this problem and likely results from calculation errors. Remember this strategy for ratio problems: always introduce a variable to represent the common factor, use the given relationship to find that factor, then calculate the specific values you need. This systematic approach prevents mix-ups between the different numbers in the ratio.

Question 9

A solution contains alcohol and water in the ratio $3:7$ . If $20$ liters of water are added to the solution, the ratio becomes $3:11$ . What was the original volume of the solution?

$40$ liters
$50$ liters (correct answer)
$60$ liters
$35$ liters
$70$ liters

Explanation: When you encounter ratio problems involving changes to quantities, the key is to set up equations that represent both the original and new situations using the same variables. Let's say the original solution has

3x

liters of alcohol and

7x

liters of water, where

x

is our scaling factor. This gives us a total original volume of

10x

liters and maintains the

3:7

ratio. When 20 liters of water are added, we have

3x

liters of alcohol and

7x + 20

liters of water. The new ratio is

3:11

, so we can write:

\frac{3x}{7x + 20} = \frac{3}{11}

Cross-multiplying:

3x \cdot 11 = 3(7x + 20)

Simplifying:

33x = 21x + 60

Solving:

12x = 60

, so

x = 5

Therefore, the original volume was

10x = 10(5) = 50

liters. Let's check the wrong answers: Choice (A) 40 liters would mean

x = 4

, giving us 12 liters alcohol and 28 liters water initially. Adding 20 liters of water creates a ratio of

12:48 = 1:4

, not

3:11

. Choice (C) 60 liters means

x = 6

, creating an initial ratio that doesn't work with our constraint. Choice (D) 35 liters doesn't fit our

10x

pattern since 35 isn't divisible by 10. Study tip: In ratio problems with added quantities, always define your variables clearly and remember that ratios scale proportionally—use a common factor to represent both parts of the original ratio.

Question 10

In a parking lot, the ratio of cars to trucks to motorcycles is $8:5:2$ . If there are $24$ motorcycles, how many more cars are there than trucks?

$36$ (correct answer)
$60$
$96$
$156$
$216$

Explanation: When you encounter ratio problems, your first step is finding the value of each "part" in the ratio by using the given information about one quantity. The ratio

8:5:2

tells you that for every 8 cars, there are 5 trucks and 2 motorcycles. Since there are 24 motorcycles, you can find how many "parts" this represents:

24 \div 2 = 12

parts. This means each part of the ratio equals 12 vehicles. Now you can find the actual numbers: cars =

8 \times 12 = 96

, trucks =

5 \times 12 = 60

, and motorcycles =

2 \times 12 = 24

(which confirms our calculation). The difference between cars and trucks is

96 - 60 = 36

. Looking at the wrong answers: Choice B (60) gives you the total number of trucks, not the difference between cars and trucks. Choice C (96) is the total number of cars, which you'd get if you forgot to subtract the trucks. Choice D (156) is the sum of cars and trucks (

96 + 60

), which might result from misreading "more than" as "plus." The correct answer is A. Strategy tip: In ratio problems, always identify what each "part" represents by dividing the known quantity by its ratio number. Then multiply each ratio component by this value to find all quantities. Finally, double-check that you're answering the specific question asked—here it's the difference, not individual totals.

Question 11

The ratio of length to width of a rectangle is $5:3$ . If the perimeter is $64$ units, what is the area of the rectangle?

$240$ square units (correct answer)
$300$ square units
$180$ square units
$320$ square units
$400$ square units

Explanation: When you encounter ratio and perimeter problems, you're working with proportional relationships and the fundamental properties of geometric shapes. The key is translating the ratio into actual measurements using the given constraint. Since the length-to-width ratio is

5:3

, you can express the dimensions as

5x

and

3x

for some multiplier

x

. The perimeter formula for a rectangle is

P = 2l + 2w

, so:

64 = 2(5x) + 2(3x) = 10x + 6x = 16x

. Solving gives

x = 4

, making the length

5(4) = 20

units and width

3(4) = 12

units. The area is

20 \times 12 = 240

square units. Looking at the wrong answers: Choice B (

300

) likely comes from incorrectly using

x = 5

, which would give dimensions of

25 \times 12

, but this doesn't satisfy the perimeter constraint. Choice C (

180

) might result from calculation errors or using incorrect dimensions like

15 \times 12

. Choice D (

320

) could come from multiplying the perimeter by an incorrect factor or making arithmetic mistakes in the setup. The correct answer is A. Strategy tip: Always use variables to represent ratio parts, then use the given constraint (perimeter, area, etc.) to solve for the multiplier. Double-check by verifying both the ratio and the constraint are satisfied by your final dimensions. This systematic approach prevents the calculation errors that create most wrong answer choices in ratio problems.

Question 12

A recipe for trail mix uses nuts, raisins, and chocolate chips in the ratio $4:3:2$ . If you want to make $18$ cups of trail mix, how many cups of nuts do you need?

$8$ cups of nuts needed (correct answer)
$6$ cups of nuts needed
$9$ cups of nuts needed
$4$ cups of nuts needed
$12$ cups of nuts needed

Explanation: When you encounter ratio problems, you're working with proportional relationships between different parts of a whole. The key insight is that ratios tell you the relative amounts, not the actual amounts, so you need to scale them up to match your target total. The ratio

4:3:2

means that for every 4 parts nuts, there are 3 parts raisins and 2 parts chocolate chips. First, find the total number of parts:

4 + 3 + 2 = 9

parts total. Since you want 18 cups of trail mix, each "part" represents

18 \div 9 = 2

cups. Therefore, nuts need

4 \times 2 = 8

cups. Looking at the wrong answers: Choice B (6 cups) likely comes from confusing nuts with raisins—if you mistakenly thought nuts were 3 parts instead of 4, you'd get

3 \times 2 = 6

cups. Choice C (9 cups) represents a common error where students might think nuts are half of the total (

18 \div 2 = 9

), misunderstanding how ratios work. Choice D (4 cups) occurs when students use the ratio number directly without scaling—they see "4" in the ratio and assume that's the answer, forgetting that ratios must be proportionally adjusted to match the desired total. The correct answer is A: 8 cups of nuts. Study tip: For ratio problems, always follow this three-step process: add up all ratio parts, divide your target total by this sum to find the value of one part, then multiply by the specific ratio number you need. This systematic approach prevents the scaling errors that create most wrong answers.

Question 13

A mixture contains three chemicals A, B, and C in the ratio $2:4:3$ . If the total amount of the mixture is $54$ grams and $6$ grams of chemical C are removed, what is the ratio of A to B in the remaining mixture?

$1:2$ (correct answer)
$2:3$
$3:4$
$6:11$
$12:24$

Explanation: When you encounter ratio problems where quantities are removed, focus on finding the actual amounts first, then determining what remains. Start with the original ratio

2:4:3

for chemicals A, B, and C. Since ratios represent proportional parts, you can think of this as

2x + 4x + 3x = 9x

total parts. With

54

grams total, you have

9x = 54

, so

x = 6

grams per part. This means the original mixture contains:

Chemical A: $2 \times 6 = 12$ grams
Chemical B: $4 \times 6 = 24$ grams
Chemical C: $3 \times 6 = 18$ grams

After removing

6

grams of chemical C, you're left with:

Chemical A: $12$ grams (unchanged)
Chemical B: $24$ grams (unchanged)
Chemical C: $18 - 6 = 12$ grams

The ratio of A to B in the remaining mixture is

12:24

, which simplifies to

1:2

. Choice A is correct. Choice B (

2:3

) incorrectly uses the original ratio parts for A and C. Choice C (

3:4

) mistakenly compares the remaining amounts of C to B. Choice D (

6:11

) appears to use the individual amounts without proper simplification or represents a calculation error. Strategy tip: In ratio problems involving removal, always convert ratios to actual quantities first, apply the changes, then find the new ratio. Don't try to work directly with ratio parts when quantities change.

Question 14

The ratio of Sarah's age to her mother's age is $3:8$ . If the sum of their ages is $44$ years, what is Sarah's age?

$12$ years old currently (correct answer)
$16$ years old currently
$32$ years old currently
$24$ years old currently
$18$ years old currently

Explanation: When you encounter ratio problems combined with sum constraints, you're dealing with a system where the parts must add up to a known total. The key insight is that ratios tell you the relative sizes, not the actual values. Given that Sarah's age to her mother's age is

3:8

, you can think of Sarah's age as

3x

and her mother's age as

8x

for some multiplier

x

. Since their ages sum to 44 years, you have:

3x + 8x = 44

, which simplifies to

11x = 44

. Solving gives

x = 4

. Therefore, Sarah's age is

3x = 3(4) = 12

years old. Let's check why the other answers don't work. Choice B (16 years) would mean the mother is about 35 years old (since

16 + 35 = 51 \neq 44

), and the ratio

16:35

doesn't simplify to

3:8

. Choice C (32 years) would require the mother to be 12 years old for the sum to work, but then Sarah would be older than her mother, which contradicts the

3:8

ratio where Sarah should be younger. Choice D (24 years) would make the mother 20 years old, giving a ratio of

24:20 = 6:5

, not

3:8

. The correct answer is A. Strategy tip: In ratio problems with sums, always use a variable multiplier for the ratio parts, then set up an equation with the given total. This systematic approach prevents arithmetic errors and makes verification straightforward.

Question 15

The angles of a triangle are in the ratio $2:3:4$ . What is the measure of the largest angle?

$80°$ (correct answer)
$90°$
$72°$
$60°$
$40°$

Explanation: When you encounter a triangle problem involving angle ratios, remember that all triangles have interior angles that sum to

180°

. This fundamental property is your key to solving ratio problems. Given that the angles are in the ratio

2:3:4

, you can represent the three angles as

2x

3x

, and

4x

for some value

x

. Since these must sum to

180°

2x + 3x + 4x = 180°

9x = 180°

x = 20°

Therefore, the three angles measure

2x = 40°

3x = 60°

, and

4x = 80°

. The largest angle is

80°

. Looking at the wrong answers: Choice B (

90°

) would make this a right triangle, but the ratio

2:3:4

doesn't produce a right angle. Choice C (

72°

) might tempt you if you incorrectly calculated

x

or confused which angle corresponds to which part of the ratio. Choice D (

60°

) represents the middle angle in our solution, not the largest one—this tests whether you can identify which angle the question asks for. The correct answer is A)

80°

. Strategy tip: For any triangle angle ratio problem, set up the equation by letting the angles be multiples of an unknown variable, then use the

180°

sum rule. Always double-check which angle the question asks for—smallest, largest, or middle—since test makers often include the other angles as distractors.

Question 16

A bag contains marbles in three colors with quantities in the ratio $4:6:5$ . If $3$ marbles of each color are added to the bag, which of the following could be the new ratio?

$7:9:8$ (correct answer)
$5:8:6$
$4:6:5$
$1:2:1$
$8:12:10$

Explanation: When you encounter ratio problems involving changes to quantities, you need to work with actual numbers, not just the ratio itself, since adding the same amount to different quantities changes their proportional relationships. Let's say the original quantities are

4x

6x

, and

5x

marbles for some value

x

. After adding 3 marbles of each color, the new quantities become

(4x + 3)

(6x + 3)

, and

(5x + 3)

. To check option A (

7:9:8

), we need:

\frac{4x + 3}{7} = \frac{6x + 3}{9} = \frac{5x + 3}{8}

From the first two ratios:

9(4x + 3) = 7(6x + 3)

36x + 27 = 42x + 21

6 = 6x

, so

x = 1

Let's verify with the third ratio:

\frac{5(1) + 3}{8} = \frac{8}{8} = 1

, and

\frac{4(1) + 3}{7} = \frac{7}{7} = 1

✓ Option B (

5:8:6

) would require solving

5(6x + 3) = 8(4x + 3)

, giving

30x + 15 = 32x + 24

, so

x = -4.5

. Since quantities must be positive, this is impossible. Option C (

4:6:5

) would mean the ratio stays unchanged after adding marbles, which only happens if you add proportional amounts. Since we're adding 3 to each color (not proportional to

4:6:5

), this can't work. Option D (

1:2:1

) leads to contradictory equations when you try to solve for

x

. Remember: when quantities change by fixed amounts, always convert ratios to actual expressions with variables, then solve algebraically to check if a solution exists.

Question 17

A recipe calls for ingredients A, B, and C in the ratio $2:5:3$ . If you want to make a batch that uses exactly $15$ units of ingredient B, how many units of ingredient C will you need?

$9$ units of ingredient C (correct answer)
$6$ units of ingredient C
$12$ units of ingredient C
$10$ units of ingredient C
$18$ units of ingredient C

Explanation: When you encounter ratio problems, you're working with proportional relationships between quantities. The key insight is that ratios tell you the relative amounts, and you can scale them up or down while maintaining the same proportions. Given the ratio

2:5:3

for ingredients A, B, and C, this means for every 2 units of A, you need 5 units of B and 3 units of C. Since you want exactly 15 units of ingredient B, you need to find the scaling factor. The ratio shows B should be 5 units, but you want 15 units, so your scaling factor is

15 ÷ 5 = 3

. This means you're making 3 times the base recipe. Therefore, ingredient C needs

3 × 3 = 9

units. Looking at the wrong answers: Choice B (6 units) represents what you'd get if you incorrectly used a scaling factor of 2 instead of 3. Choice C (12 units) might result from confusing the ratio positions or using faulty arithmetic. Choice D (10 units) doesn't correspond to any logical scaling of the given ratio. Choice A (9 units) correctly applies the scaling factor of 3 to ingredient C's ratio value of 3. Strategy tip: In ratio problems, always identify what you know and what you need to find, then determine the scaling factor by comparing the given amount to the ratio value for that same ingredient. Apply this same scaling factor to find the unknown quantities.

Question 18

The ratio of the number of pages Tom read on Monday to Tuesday to Wednesday was $3:4:5$ . If he read a total of $84$ pages over the three days, and on Thursday he read twice as many pages as he did on Monday, how many pages did Tom read on Thursday?

$21$
$28$
$35$
$42$ (correct answer)
$56$

Explanation: When you encounter ratio problems with totals, the key is converting ratios into actual quantities by finding the value of each ratio part. The ratio

3:4:5

means Tom read

3x

pages Monday,

4x

pages Tuesday, and

5x

pages Wednesday, where

x

is some unknown multiplier. Since these three days total

84

pages, you can write:

3x + 4x + 5x = 84

. This simplifies to

12x = 84

, so

x = 7

. Now you know the actual pages for each day: Monday =

3(7) = 21

pages, Tuesday =

4(7) = 28

pages, Wednesday =

5(7) = 35

pages. Thursday he read twice Monday's amount:

2 \times 21 = 42

pages. Choice A (

21

) is Monday's reading amount, not Thursday's. This traps students who identify Monday correctly but forget the final step. Choice B (

28

) is Tuesday's amount—you might select this if you confuse which day the question asks about. Choice C (

35

) is Wednesday's reading amount, another day-confusion trap. Choice D (

42

) correctly doubles Monday's total. The correct answer is D. Remember this two-step approach for ratio problems: first find the multiplier by setting up an equation with the total, then use that multiplier to find individual quantities. Always double-check which specific quantity the question asks for—ratio problems often include extra information that creates tempting wrong answers.

Question 19

In a bag of marbles, the ratio of red marbles to blue marbles to green marbles is $4:6:5$ . If there are $18$ blue marbles in the bag, what is the total number of marbles?

$30$ marbles total
$45$ marbles total (correct answer)
$54$ marbles total
$42$ marbles total
$27$ marbles total

Explanation: When you encounter a ratio problem with a known quantity, you need to use the ratio as a scale factor to find all other quantities. The ratio

4:6:5

tells you that for every 4 red marbles, there are 6 blue marbles and 5 green marbles. Since you know there are 18 blue marbles, you can find the scale factor by comparing the actual blue marbles to the ratio amount:

18 ÷ 6 = 3

. This means the ratio has been multiplied by 3. Now apply this scale factor to all parts of the ratio:

Red marbles: $4 × 3 = 12$
Blue marbles: $6 × 3 = 18$ ✓ (matches given information)
Green marbles: $5 × 3 = 15$

Total marbles:

12 + 18 + 15 = 45

Choice A (30) represents a common error where students might add the ratio numbers (4 + 6 + 5 = 15) and then double it, incorrectly thinking this accounts for the scaling. Choice C (54) could result from mistakenly using 18 as the scale factor itself, then multiplying the sum of ratio parts:

(4 + 6 + 5) × 18 ÷ 5 = 54

. Choice D (42) might come from incorrectly calculating the scale factor as 18 ÷ 4 = 4.5, then applying it inconsistently. Strategy tip: Always verify your scale factor by checking that it gives you the known quantity when applied to the corresponding ratio part. This catch errors early and builds confidence in your solution.

Question 20

The weights of three packages are in the ratio $5:7:8$ . If the heaviest package weighs $12$ pounds more than the lightest package, what is the weight of the middle package?

$28$ pounds (correct answer)
$20$ pounds
$32$ pounds
$24$ pounds
$35$ pounds

Explanation: When you encounter ratio problems, you're working with proportional relationships where the actual values are multiples of the ratio terms. Here, the weights are in the ratio

5:7:8

, meaning you can express them as

5x

7x

, and

8x

for some unknown multiplier

x

. The heaviest package weighs

8x

pounds and the lightest weighs

5x

pounds. Since the difference is 12 pounds, you can write:

8x - 5x = 12

, which simplifies to

3x = 12

. Therefore,

x = 4

. Now you can find all three weights: lightest =

5(4) = 20

pounds, middle =

7(4) = 28

pounds, and heaviest =

8(4) = 32

pounds. The middle package weighs 28 pounds. Looking at the wrong answers: Choice B (

20

pounds) gives you the weight of the lightest package—a common trap when students mix up which weight the question asks for. Choice C (

32

pounds) is the weight of the heaviest package, another position mix-up. Choice D (

24

pounds) might result from calculation errors, perhaps incorrectly setting up the equation or making arithmetic mistakes with the multiplier. The correct answer is A. Strategy tip: In ratio problems, always define your unknown multiplier clearly and double-check which quantity the question asks for. Students often solve correctly but report the wrong value from their work. After finding all values, verify your ratios match the original relationship.