Praxis Math Quiz: Solve Ratio Problems
20 questions · exam conditions
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Solve Ratio ProblemsQuestion 1 of 20

In a certain classroom, the ratio of students who prefer fiction to students who prefer nonfiction is 5 to 3. If there are 32 students in the classroom, how many more students prefer fiction than nonfiction?

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Praxis Math Quiz

Praxis Math Quiz: Solve Ratio Problems

Practice Solve Ratio Problems in Praxis Math 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 Solve Ratio Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

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

In a certain classroom, the ratio of students who prefer fiction to students who prefer nonfiction is 5 to 3. If there are 32 students in the classroom, how many more students prefer fiction than nonfiction?

  1. 2
  2. 4
  3. 8 (correct answer)
  4. 20
Explanation: The ratio of fiction to nonfiction is 5:3. This means there are 5+3=85+3=8 total parts in the ratio. The 32 students represent these 8 parts. To find the number of students per part, divide the total students by the total parts: 32÷8=432 \div 8 = 4 students per part. The number of students who prefer fiction is 5 parts×4studentspart=205 \text{ parts} \times 4 \frac{\text{students}}{\text{part}} = 20 students. The number who prefer nonfiction is 3 parts×4studentspart=123 \text{ parts} \times 4 \frac{\text{students}}{\text{part}} = 12 students. The question asks for how many more students prefer fiction, which is the difference: 20−12=820 - 12 = 8.

Question 2

A bag contains only red and blue marbles in a ratio of 3:7 (red to blue). If the bag contains a total of 80 marbles, how many red marbles must be added to the bag so that the ratio of red marbles to blue marbles becomes 1:2?

  1. 4 (correct answer)
  2. 8
  3. 24
  4. 28
Explanation: First, find the initial number of red and blue marbles. The total number of parts in the ratio is 3+7=103+7=10. With 80 marbles total, each part represents 80÷10=880 \div 10 = 8 marbles. Initial red marbles: 3×8=243 \times 8 = 24. Initial blue marbles: 7×8=567 \times 8 = 56. Next, let xx be the number of red marbles to add. The number of blue marbles stays at 56. The new ratio is 24+x56=12\frac{24+x}{56} = \frac{1}{2}. Cross-multiply to solve for xx: 2(24+x)=562(24+x) = 56, which gives 48+2x=5648+2x=56. Subtracting 48 from both sides gives 2x=82x=8, so x=4x=4. 4 red marbles must be added.

Question 3

A map has a scale where 2 inches represents 75 miles. The distance on the map between two cities is 5.5 inches. A driver averages 60 miles per hour. How long will the drive between the two cities take?

  1. 3 hours, 26 minutes (correct answer)
  2. 3 hours, 44 minutes
  3. 4 hours, 24 minutes
  4. 2 hours, 5 minutes
Explanation: First, find the actual distance in miles. Set up a proportion: 2 inches75 miles=5.5 inchesx miles\frac{2 \text{ inches}}{75 \text{ miles}} = \frac{5.5 \text{ inches}}{x \text{ miles}}. Cross-multiply: 2x=75×5.5=412.52x = 75 \times 5.5 = 412.5. Solve for xx: x=206.25x = 206.25 miles. Next, use the formula Time = Distance / Speed. Time = 206.25 miles60 mph=3.4375\frac{206.25 \text{ miles}}{60 \text{ mph}} = 3.4375 hours. To convert this to hours and minutes, the whole number is the hours (3 hours). Convert the decimal part to minutes: 0.4375 hours×60minuteshour=26.250.4375 \text{ hours} \times 60 \frac{\text{minutes}}{\text{hour}} = 26.25 minutes. Rounded to the nearest minute, this is 26 minutes. The total time is 3 hours and 26 minutes.

Question 4

A painter is mixing paint to create a specific shade of green. The ratio of blue paint to yellow paint is 2:5. If the painter needs to make 21 gallons of green paint in total, how many more gallons of yellow paint are used than blue paint?

  1. 3
  2. 6
  3. 9 (correct answer)
  4. 15
Explanation: The ratio of blue to yellow paint is 2:5. The total number of parts in the mixture is 2+5=72+5=7 parts. The total volume is 21 gallons. To find the volume of one part, divide the total volume by the total number of parts: 21 gallons÷7 parts=321 \text{ gallons} \div 7 \text{ parts} = 3 gallons per part. The amount of blue paint is 2 parts×3gallonspart=62 \text{ parts} \times 3 \frac{\text{gallons}}{\text{part}} = 6 gallons. The amount of yellow paint is 5 parts×3gallonspart=155 \text{ parts} \times 3 \frac{\text{gallons}}{\text{part}} = 15 gallons. The question asks for the difference: 15−6=915 - 6 = 9 gallons. Alternatively, the difference in parts is 5−2=35-2=3 parts. The difference in gallons is 3 parts×3gallonspart=93 \text{ parts} \times 3 \frac{\text{gallons}}{\text{part}} = 9 gallons.

Question 5

At a factory, Machine A produces widgets at a rate such that for every 4 widgets it produces, Machine B produces 3. If the two machines work together and produce a total of 1,050 widgets, how many widgets were produced by Machine A?

  1. 450
  2. 525
  3. 600 (correct answer)
  4. 750
Explanation: The ratio of production for Machine A to Machine B is 4:3. For every cycle, 4+3=74+3=7 widgets are produced in total. To find out how many cycles occurred to produce 1,050 widgets, divide the total by the number of widgets per cycle: 1050÷7=1501050 \div 7 = 150 cycles. Machine A produces 4 widgets per cycle, so its total production is 150 cycles×4widgetscycle=600150 \text{ cycles} \times 4 \frac{\text{widgets}}{\text{cycle}} = 600 widgets.

Question 6

The ratio of the number of apples to the number of oranges in a basket is 3:5. The ratio of the number of oranges to the number of pears is 2:3. If there are 30 pears in the basket, how many apples are there?

  1. 12 (correct answer)
  2. 15
  3. 18
  4. 20
Explanation: Let A, O, and P be the number of apples, oranges, and pears. We are given AO=35\frac{A}{O} = \frac{3}{5} and OP=23\frac{O}{P} = \frac{2}{3}. We are also given P=30P=30. First, use the second ratio to find the number of oranges. O30=23\frac{O}{30} = \frac{2}{3}. Cross-multiply: 3O=30×2=603O = 30 \times 2 = 60, so O=20O=20. Now use the first ratio to find the number of apples. A20=35\frac{A}{20} = \frac{3}{5}. Cross-multiply: 5A=20×3=605A = 20 \times 3 = 60, so A=12A=12. There are 12 apples.

Question 7

In a school election, two candidates, Alex and Ben, received votes in the ratio of 5:3. If Alex received 240 more votes than Ben, how many total votes were cast?

  1. 384
  2. 640
  3. 960 (correct answer)
  4. 1200
Explanation: Let the number of votes for Alex be 5x5x and for Ben be 3x3x. The difference in votes is 5x−3x=2x5x - 3x = 2x. We are told this difference is 240 votes. So, 2x=2402x = 240, which means x=120x=120. The total number of votes cast is the sum of the votes for both candidates, which is 5x+3x=8x5x + 3x = 8x. Substitute the value of xx: Total votes = 8×120=9608 \times 120 = 960.

Question 8

A city has a population of 80,000 and an area of 50 square miles. A neighboring city has a population of 120,000 and an area of 75 square miles. What is the ratio of the population density of the first city to the population density of the second city?

  1. 1:1 (correct answer)
  2. 2:3
  3. 3:2
  4. 4:5
Explanation: Population density is calculated as Population / Area. For the first city: Density₁ = 80,00050=1,600\frac{80,000}{50} = 1,600 people per square mile. For the second city: Density₂ = 120,00075=1,600\frac{120,000}{75} = 1,600 people per square mile. The ratio of the population density of the first city to the second city is 16001600\frac{1600}{1600}, which simplifies to 1:1.

Question 9

A wildlife biologist catches, tags, and releases 80 deer in a forest. A month later, she catches a sample of 150 deer and finds that 12 of them have tags. What is the most reasonable estimate for the total deer population in the forest?

  1. 800
  2. 1000 (correct answer)
  3. 1200
  4. 1500
Explanation: This is a capture-recapture problem that can be solved with a proportion. The ratio of tagged deer to the total population should be approximately equal to the ratio of tagged deer in the sample to the sample size. Let PP be the total deer population. Tagged in populationTotal population=Tagged in sampleSample size\frac{\text{Tagged in population}}{\text{Total population}} = \frac{\text{Tagged in sample}}{\text{Sample size}}. Plugging in the numbers: 80P=12150\frac{80}{P} = \frac{12}{150}. To solve for PP, cross-multiply: 12P=80×150=1200012P = 80 \times 150 = 12000. Divide by 12: P=1200012=1000P = \frac{12000}{12} = 1000. The estimated total deer population is 1000.

Question 10

Two rectangular gardens are geometrically similar. The ratio of the lengths of their corresponding sides is 3 to 5. If the area of the smaller garden is 72 square feet, what is the area of the larger garden in square feet?

  1. 120
  2. 200 (correct answer)
  3. 43.2
  4. 648
Explanation: When two figures are similar, the ratio of their areas is the square of the ratio of their corresponding side lengths. The ratio of the sides is 3:5. Therefore, the ratio of the areas is 32:523^2:5^2, which is 9:25. Let AlargeA_{large} be the area of the larger garden. We can set up the proportion: AreasmallArealarge=925\frac{\text{Area}_{small}}{\text{Area}_{large}} = \frac{9}{25}. Substituting the given area of the smaller garden: 72Alarge=925\frac{72}{A_{large}} = \frac{9}{25}. To solve for AlargeA_{large}, cross-multiply: 9×Alarge=72×259 \times A_{large} = 72 \times 25. Divide by 9: Alarge=729×25=8×25=200A_{large} = \frac{72}{9} \times 25 = 8 \times 25 = 200. The area of the larger garden is 200 square feet.

Question 11

A recipe for 12 cookies requires 34\frac{3}{4} cup of sugar. A baker needs to make 90 cookies for a catering event. If sugar is only sold in full 1-cup bags, what is the minimum number of bags of sugar the baker must purchase?

  1. 5 bags
  2. 6 bags (correct answer)
  3. 7 bags
  4. 8 bags
Explanation: First, set up a proportion to find the total amount of sugar needed. Let xx be the cups of sugar for 90 cookies. 34 cup12 cookies=x cups90 cookies\frac{\frac{3}{4} \text{ cup}}{12 \text{ cookies}} = \frac{x \text{ cups}}{90 \text{ cookies}}. Solving for xx: 12x=90×3412x = 90 \times \frac{3}{4}, which simplifies to 12x=2704=67.512x = \frac{270}{4} = 67.5. Divide by 12: x=67.512=5.625x = \frac{67.5}{12} = 5.625 cups. Since sugar is sold in full 1-cup bags, the baker cannot buy a fraction of a bag. The baker needs 5.625 cups, so they must purchase 6 full bags to have enough.

Question 12

A total of $5,400 is to be distributed among three people—Ava, Ben, and Carla—in the ratio 2:3:4, respectively. After the initial distribution, Carla gives a portion of her share to Ava so that Ava and Ben have the same amount of money. How much money did Carla give to Ava?

  1. $300
  2. $600 (correct answer)
  3. $900
  4. $1,200
Explanation: First, determine each person's initial share. The ratio is 2:3:4, so there are 2+3+4=9 total parts. The value of one part is $5,400÷9 = 600.Ava′sshare:2×600. Ava's share: 2×600 = 1,200.Ben′sshare:3×1,200. Ben's share: 3×600 = 1,800.Carla′sshare:4×1,800. Carla's share: 4×600 = $2,400. For Ava to have the same amount as Ben, she needs $1,800. She currently has $1,200, so she needs an additional $1,800 - $1,200 = $600. Therefore, Carla gives $600 to Ava.

Question 13

In a company, the ratio of managers to directors is 4:3, and the ratio of directors to administrative assistants is 6:7. If there are 35 administrative assistants, what is the total number of these three types of employees?

  1. 70
  2. 85
  3. 105 (correct answer)
  4. 120
Explanation: First, find the number of directors (D) using the ratio with administrative assistants (A). DA=67\frac{D}{A} = \frac{6}{7}. Given A=35A=35, we have D35=67\frac{D}{35} = \frac{6}{7}. Cross-multiply: 7D=35×6=2107D = 35 \times 6 = 210, so D=30D = 30. Now find the number of managers (M) using the ratio with directors. MD=43\frac{M}{D} = \frac{4}{3}. With D=30D=30, we have M30=43\frac{M}{30} = \frac{4}{3}. Cross-multiply: 3M=30×4=1203M = 30 \times 4 = 120, so M=40M = 40. The total number of employees is the sum of the three groups: M+D+A=40+30+35=105M+D+A = 40 + 30 + 35 = 105.

Question 14

To make a certain type of concrete, the ratio of cement to sand to gravel by weight is 2:3:5. A construction crew needs to make 1,500 pounds of this concrete. How many more pounds of gravel are needed than cement?

  1. 300
  2. 450 (correct answer)
  3. 600
  4. 750
Explanation: The ratio is 2:3:5. The total number of parts is 2+3+5=102+3+5=10. The total weight of the concrete is 1,500 pounds. The weight of one part is 1,500 lbs10 parts=150\frac{1,500 \text{ lbs}}{10 \text{ parts}} = 150 pounds per part. The weight of cement is 2 parts×150lbspart=3002 \text{ parts} \times 150 \frac{\text{lbs}}{\text{part}} = 300 pounds. The weight of gravel is 5 parts×150lbspart=7505 \text{ parts} \times 150 \frac{\text{lbs}}{\text{part}} = 750 pounds. The difference between the weight of gravel and cement is 750−300=450750 - 300 = 450 pounds. Alternatively, the difference in parts is 5−2=35-2=3 parts. The difference in weight is 3 parts×150lbspart=4503 \text{ parts} \times 150 \frac{\text{lbs}}{\text{part}} = 450 pounds.

Question 15

If 5 machines can produce 300 widgets in 6 hours, how many hours would it take for 8 machines to produce 480 widgets, assuming all machines work at the same constant rate?

  1. 4
  2. 6 (correct answer)
  3. 8
  4. 10
Explanation: First, find the production rate of a single machine. If 5 machines produce 300 widgets in 6 hours, then one machine produces 3005=60\frac{300}{5} = 60 widgets in 6 hours. The rate for one machine is 60 widgets6 hours=10\frac{60 \text{ widgets}}{6 \text{ hours}} = 10 widgets per hour. Now, find how long it would take 8 machines to produce 480 widgets. The combined rate of 8 machines is 8 machines×10widgets/hrmachine=808 \text{ machines} \times 10 \frac{\text{widgets/hr}}{\text{machine}} = 80 widgets per hour. The time required is Total Widgets / Rate = 480 widgets80 widgets/hr=6\frac{480 \text{ widgets}}{80 \text{ widgets/hr}} = 6 hours.

Question 16

A bronze alloy is made from copper and tin in the ratio 11:1 by mass. If a statue made of this alloy contains 24 kilograms of tin, what is the total mass of the statue?

  1. 264 kg
  2. 288 kg (correct answer)
  3. 300 kg
  4. 312 kg
Explanation: The ratio of copper to tin is 11:1. This means there are 11 parts copper for every 1 part tin. The total number of parts in the alloy is 11+1=1211+1=12. We are told that the 1 part of tin corresponds to a mass of 24 kilograms. Therefore, the mass of one part is 24 kg. The total mass of the statue corresponds to 12 parts. So, the total mass is 12 parts×24kgpart=28812 \text{ parts} \times 24 \frac{\text{kg}}{\text{part}} = 288 kg.

Question 17

The ratio of width to length of a rectangular banner is 2:7. If the perimeter of the banner is 108 inches, what is the length of the banner in inches?

  1. 12
  2. 24
  3. 42 (correct answer)
  4. 84
Explanation: Let the width be 2x2x and the length be 7x7x. The perimeter of a rectangle is given by the formula P=2(W+L)P = 2(W+L). We are given P=108P=108. So, 108=2(2x+7x)108 = 2(2x+7x). Simplify the expression in the parentheses: 108=2(9x)108 = 2(9x), which is 108=18x108 = 18x. Solve for xx by dividing by 18: x=10818=6x = \frac{108}{18} = 6. The question asks for the length of the banner, which is 7x7x. So, the length is 7×6=427 \times 6 = 42 inches.

Question 18

A sum of money was shared between Liam and Mia in the ratio 5:8. Mia received $21 more than Liam. What was the total sum of money shared?

  1. $49
  2. $56
  3. $91 (correct answer)
  4. $105
Explanation: The ratio of Liam's share to Mia's share is 5:8. Let Liam's share be 5x5x and Mia's share be 8x8x. The difference in their shares is 8x−5x=3x8x - 5x = 3x. We are told this difference is $21. So, (3x = 21\), which means \(x = 7). The total sum of money is the sum of their shares, which is 5x+8x=13x5x + 8x = 13x. Substitute the value of xx: Total sum = (13 \times 7=7 = 91).

Question 19

If 3a=4b3a = 4b and 5b=6c5b = 6c, what is the ratio of aa to cc?

  1. 5:8
  2. 8:5 (correct answer)
  3. 2:1
  4. 1:2
Explanation: From 3a=4b3a = 4b, we can write the ratio ab=43\frac{a}{b} = \frac{4}{3}. From 5b=6c5b = 6c, we can write the ratio bc=65\frac{b}{c} = \frac{6}{5}. To find the ratio of aa to cc, we can multiply these two ratios: ac=ab×bc\frac{a}{c} = \frac{a}{b} \times \frac{b}{c}. Substituting the values: ac=43×65=2415\frac{a}{c} = \frac{4}{3} \times \frac{6}{5} = \frac{24}{15}. This fraction simplifies by dividing the numerator and denominator by their greatest common divisor, 3. 24÷315÷3=85\frac{24 \div 3}{15 \div 3} = \frac{8}{5}. Therefore, the ratio of aa to cc is 8:5.

Question 20

A 6-foot-tall person casts a shadow that is 9 feet long. At the same time, a nearby flagpole casts a shadow that is 30 feet long. What is the height of the flagpole in yards?

  1. 20
  2. 13.3
  3. 10
  4. 6.7 (correct answer)
Explanation: The ratio of an object's height to its shadow's length is constant. Let hh be the height of the flagpole in feet. Set up the proportion: person’s heightperson’s shadow=flagpole’s heightflagpole’s shadow\frac{\text{person's height}}{\text{person's shadow}} = \frac{\text{flagpole's height}}{\text{flagpole's shadow}}. So, 6 ft9 ft=h30 ft\frac{6 \text{ ft}}{9 \text{ ft}} = \frac{h}{30 \text{ ft}}. Simplify the ratio 69\frac{6}{9} to 23\frac{2}{3}. Now we have 23=h30\frac{2}{3} = \frac{h}{30}. Cross-multiply: 3h=2×30=603h = 2 \times 30 = 60. Solve for hh: h=20h = 20 feet. The question asks for the height in yards. Since there are 3 feet in 1 yard, divide the height in feet by 3: 20 feet÷3feetyard≈6.6720 \text{ feet} \div 3 \frac{\text{feet}}{\text{yard}} \approx 6.67 yards. Rounded to one decimal place, this is 6.7 yards.