ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Equations With Fractions And Decimals

20 questions · exam conditions

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Equations With Fractions And DecimalsQuestion 1 of 20

The equation $0.2(y - 5) + 0.3 = 1.7$ is given. What is the value of $y$ ?

7

8.5

12

15

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ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Equations With Fractions And Decimals

Practice Equations With Fractions And Decimals in ACCUPLACER Quantitative Reasoning, Algebra & Statistics 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 Equations With Fractions And Decimals, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

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

The equation $0.2(y - 5) + 0.3 = 1.7$ is given. What is the value of $y$ ?

$7$
$8.5$
$12$ (correct answer)
$15$

Explanation: First, isolate the term containing the parentheses by subtracting 0.3 from both sides:

0.2(y - 5) = 1.7 - 0.3

, which simplifies to

0.2(y - 5) = 1.4

. Next, divide both sides by 0.2:

y - 5 = \frac{1.4}{0.2} = 7

. Finally, add 5 to both sides to solve for

y

y = 7 + 5 = 12

Question 2

A customer's monthly phone bill is calculated as a flat fee of $15.00 plus $2.50 per gigabyte of data used. If a customer's bill for one month was $52.50, how many gigabytes of data did they use?

$6$
$15$ (correct answer)
$19$
$27$

Explanation: Let

g

be the number of gigabytes of data used. The total cost can be represented by the equation

15.00 + 2.50g = 52.50

. To find

g

, first subtract the flat fee from the total bill:

2.50g = 52.50 - 15.00

, which simplifies to

2.50g = 37.50

. Then, divide the remaining cost by the price per gigabyte:

g = \frac{37.50}{2.50} = 15

. The customer used 15 gigabytes of data.

Question 3

If $4.5 + 0.2(x-1) = 6$ , what is the value of $x$ ?

$7.5$
$8.5$ (correct answer)
$12.5$
$24$

Explanation: To solve for

x

, first isolate the term containing the variable. Subtract 4.5 from both sides of the equation:

0.2(x-1) = 6 - 4.5

, which simplifies to

0.2(x-1) = 1.5

. Next, divide both sides by 0.2:

x-1 = \frac{1.5}{0.2} = 7.5

. Finally, add 1 to both sides:

x = 7.5 + 1 = 8.5

Question 4

If $x > 0$ and $\frac{x}{2} + \frac{x}{5} = 7$ , what is the value of $x$ ?

$1$
$10$ (correct answer)
$24.5$
$35$

Explanation: To solve for

x

, first clear the fractions by multiplying both sides of the equation by the least common denominator of 2 and 5, which is 10. This yields

10(\frac{x}{2}) + 10(\frac{x}{5}) = 10(7)

, which simplifies to

5x + 2x = 70

. Combine the like terms on the left side:

7x = 70

. Divide both sides by 7 to find the value of

x

x = 10

Question 5

If $m$ is a number such that $\frac{1}{5}m + \frac{2}{3}m = 13$ , what is the value of $m$ ?

$15$ (correct answer)
$10$
$5$
$26$

Explanation: To solve for

m

, first combine the terms on the left side. The least common denominator for 5 and 3 is 15. Rewrite the fractions:

\frac{3}{15}m + \frac{10}{15}m = 13

. Combine them:

\frac{13}{15}m = 13

. To isolate

m

, you can divide both sides by 13, which gives

\frac{1}{15}m = 1

. Then, multiply both sides by 15 to get

m = 15

Question 6

What is the solution to the equation $\frac{z-2}{6} + \frac{z}{4} = 5$ ?

$12.8$ (correct answer)
$8$
$4.4$
$14$

Explanation: The least common denominator of 6 and 4 is 12. Multiply every term in the equation by 12 to clear the fractions:

12(\frac{z-2}{6}) + 12(\frac{z}{4}) = 12(5)

. This simplifies to

2(z-2) + 3z = 60

. Distribute the 2:

2z - 4 + 3z = 60

. Combine the

z

terms:

5z - 4 = 60

. Add 4 to both sides:

5z = 64

. Divide by 5:

z = \frac{64}{5} = 12.8

Question 7

A student's final grade in a course is calculated as $\frac{3}{5}$ of the test average plus $\frac{2}{5}$ of the final exam score. A student has a test average of 85. If the student's final grade was 88, what was their final exam score?

$92.5$ (correct answer)
$89$
$86.5$
$95$

Explanation: Let

E

be the final exam score. The formula for the final grade is

G = \frac{3}{5}(Test Average) + \frac{2}{5}(E)

. We are given

G = 88

and Test Average = 85. Substitute these values into the equation:

88 = \frac{3}{5}(85) + \frac{2}{5}E

. First, calculate

\frac{3}{5}(85)

3 \times \frac{85}{5} = 3 \times 17 = 51

. The equation becomes

88 = 51 + \frac{2}{5}E

. Subtract 51 from both sides:

37 = \frac{2}{5}E

. To solve for

E

, multiply both sides by

\frac{5}{2}

E = 37 \times \frac{5}{2} = \frac{185}{2} = 92.5

Question 8

At a certain company, $\frac{1}{3}$ of the employees are in sales and $\frac{1}{4}$ are in management. The remaining 35 employees are in production. How many employees work at the company in total?

$49$
$60$
$70$
$84$ (correct answer)

Explanation: Let T be the total number of employees. The fraction of employees in sales and management combined is

\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}

. The remaining fraction of employees, who are in production, is

1 - \frac{7}{12} = \frac{5}{12}

. We are given that these remaining employees number 35. So,

\frac{5}{12}T = 35

. To find T, multiply both sides by

\frac{12}{5}

T = 35 \times \frac{12}{5} = 7 \times 12 = 84

Question 9

A solution contains $0.3x + 1.7 = 2.6x - 0.8$ . After converting to eliminate decimals by multiplying by 10, what equation must be solved?

$3x + 17 = 26x - 8$ (correct answer)
$30x + 17 = 26x - 8$
$3x + 170 = 26x - 80$
$3x + 17 = 260x - 8$

Explanation: Multiplying the entire equation

0.3x + 1.7 = 2.6x - 0.8

by 10 gives:

10(0.3x) + 10(1.7) = 10(2.6x) - 10(0.8)

, which becomes

3x + 17 = 26x - 8

. Choice B incorrectly multiplies 0.3 as 30, Choice C multiplies some terms by 100, Choice D incorrectly makes 2.6x into 260x.

Question 10

If $0.4(x + 10) - 0.1x = 1$ , what is the value of $x$ ?

$-30$
$-13$
$-10$ (correct answer)
$10$

Explanation: To solve for

x

, first distribute the 0.4:

0.4x + 4 - 0.1x = 1

. Combine the terms with

x

0.3x + 4 = 1

. Subtract 4 from both sides:

0.3x = -3

. Finally, divide by 0.3:

x = \frac{-3}{0.3} = -10

. Alternatively, multiply the entire equation by 10 to clear the decimals:

4(x + 10) - 1x = 10

, which becomes

4x + 40 - x = 10

, then

3x + 40 = 10

, so

3x = -30

, and

x = -10

Question 11

What value of $y$ satisfies the equation $\frac{3}{5}y - 2 = \frac{1}{3}y + 6$ ?

$2$
$15$
$30$ (correct answer)
$60$

Explanation: To solve the equation, first eliminate the fractions by multiplying every term by the least common denominator of 5 and 3, which is 15. The equation becomes

15(\frac{3}{5}y) - 15(2) = 15(\frac{1}{3}y) + 15(6)

, which simplifies to

9y - 30 = 5y + 90

. Next, gather the variable terms on one side by subtracting

5y

from both sides:

4y - 30 = 90

. Add 30 to both sides:

4y = 120

. Finally, divide by 4:

y = 30

Question 12

Solve for $z$ : $\frac{z + 5}{3} = \frac{z - 1}{2}$

$-7$
$\frac{4}{5}$
$7$
$13$ (correct answer)

Explanation: To solve this proportion, you can cross-multiply. This gives

2(z + 5) = 3(z - 1)

. Distribute the numbers on both sides:

2z + 10 = 3z - 3

. To solve for

z

, gather the

z

terms on one side and the constants on the other. Subtract

2z

from both sides:

10 = z - 3

. Add 3 to both sides:

13 = z

Question 13

If $\frac{2}{3}k - 4 = 2$ , what is the value of the expression $k - 3$ ?

$-6$
$1$
$6$ (correct answer)
$9$

Explanation: First, solve the given equation for

k

. Add 4 to both sides of

\frac{2}{3}k - 4 = 2

to get

\frac{2}{3}k = 6

. To isolate

k

, multiply both sides by the reciprocal of

\frac{2}{3}

, which is

\frac{3}{2}

. This gives

k = 6 \times \frac{3}{2} = 9

. The question asks for the value of

k - 3

. Substitute the value of

k

9 - 3 = 6

Question 14

To solve the equation $\frac{x}{4} - \frac{x}{6} = 3$ , what is the most efficient first step?

Multiply both sides of the equation by 24.
Multiply both sides of the equation by 12. (correct answer)
Subtract $\frac{x}{6}$ from $\frac{x}{4}$ by first finding a common denominator for the fractions.
Add $\frac{x}{6}$ to both sides of the equation.

Explanation: The most efficient way to solve an equation with fractions is to eliminate them by multiplying all terms by the least common denominator (LCD) of all the fractions. The denominators are 4 and 6. The least common multiple of 4 and 6 is 12. Therefore, multiplying both sides by 12 is the most efficient first step. While multiplying by 24 (a common multiple) would also work, it's less efficient as it involves larger numbers. Combining the fractions first is a valid method but generally takes more steps than clearing the fractions at the beginning.

Question 15

What is the solution to the equation $\frac{3}{4}x - 0.5 = 0.25x$ ?

$-1$
$\frac{2}{5}$
$\frac{1}{2}$
$1$ (correct answer)

Explanation: This equation contains both a fraction and decimals. It's often easiest to convert everything to one form. Converting to decimals:

\frac{3}{4}

is 0.75, so the equation becomes

0.75x - 0.5 = 0.25x

. Subtract

0.25x

from both sides:

0.50x - 0.5 = 0

. Add 0.5 to both sides:

0.50x = 0.5

. Divide by 0.5:

x = 1

. Alternatively, converting to fractions: 0.5 is

\frac{1}{2}

and 0.25 is

\frac{1}{4}

. The equation becomes

\frac{3}{4}x - \frac{1}{2} = \frac{1}{4}x

. Multiply all terms by the LCD, 4, to get

3x - 2 = x

. Subtract

x

from both sides:

2x - 2 = 0

. Add 2 to both sides:

2x = 2

. Divide by 2:

x = 1

Question 16

A rectangle has a length of $\frac{1}{2}x + 3$ units and a width of $\frac{1}{3}x - 1$ units. If the perimeter of the rectangle is 34 units, what is the value of $x$ ?

$12$
$18$ (correct answer)
$30$
$38.4$

Explanation: The formula for the perimeter of a rectangle is

P = 2(L+W)

. Substitute the given expressions:

34 = 2((\frac{1}{2}x + 3) + (\frac{1}{3}x - 1))

. First, simplify the expression inside the parentheses by combining like terms:

\frac{1}{2}x + \frac{1}{3}x = \frac{3}{6}x + \frac{2}{6}x = \frac{5}{6}x

, and

3 - 1 = 2

. The equation becomes

34 = 2(\frac{5}{6}x + 2)

. Distribute the 2:

34 = \frac{10}{6}x + 4

, which simplifies to

34 = \frac{5}{3}x + 4

. Subtract 4 from both sides:

30 = \frac{5}{3}x

. To solve for

x

, multiply both sides by

\frac{3}{5}

x = 30 \times \frac{3}{5} = 18

Question 17

The average (arithmetic mean) of three numbers is 15. The first number is $\frac{1}{2}x$ . The second number is $\frac{1}{3}x$ . The third number is 10. What is the value of $x$ ?

$6$
$30$
$36$
$42$ (correct answer)

Explanation: The average of three numbers is their sum divided by 3. The equation is

\frac{\frac{1}{2}x + \frac{1}{3}x + 10}{3} = 15

. First, multiply both sides by 3 to get the sum:

\frac{1}{2}x + \frac{1}{3}x + 10 = 45

. Subtract 10 from both sides:

\frac{1}{2}x + \frac{1}{3}x = 35

. To combine the fractions, find a common denominator (6):

\frac{3}{6}x + \frac{2}{6}x = 35

, which is

\frac{5}{6}x = 35

. To solve for

x

, multiply both sides by the reciprocal

\frac{6}{5}

x = 35 \times \frac{6}{5} = 7 \times 6 = 42

Question 18

What is the solution to the equation $\frac{2}{3}(x - 6) = \frac{1}{2}x$ ?

$-24$
$12$
$24$ (correct answer)
$36$

Explanation: To solve the equation

\frac{2}{3}(x - 6) = \frac{1}{2}x

, first distribute

\frac{2}{3}

on the left side:

\frac{2}{3}x - \frac{12}{3} = \frac{1}{2}x

, which simplifies to

\frac{2}{3}x - 4 = \frac{1}{2}x

. To eliminate the fractions, multiply all terms by the least common denominator, which is 6. This gives

6(\frac{2}{3}x) - 6(4) = 6(\frac{1}{2}x)

, which simplifies to

4x - 24 = 3x

. Subtracting

3x

from both sides gives

x - 24 = 0

. Adding 24 to both sides gives

x = 24

Question 19

What value of $p$ satisfies the equation $\frac{4p - 2}{p} = 3$ ?

$-2$
$\frac{1}{2}$
$\frac{5}{4}$
$2$ (correct answer)

Explanation: Assuming

p \neq 0

, we can solve this equation by multiplying both sides by

p

to clear the denominator. This gives

4p - 2 = 3p

. To isolate the variable

p

, subtract

3p

from both sides:

p - 2 = 0

. Finally, add 2 to both sides to find

p = 2

Question 20

A chemist mixes a quantity of a 20% acid solution with a 60% acid solution to produce 50 liters of a 30% acid solution. How many liters of the 20% acid solution were used?

$12.5$
$18.75$
$25$
$37.5$ (correct answer)

Explanation: Let

x

be the number of liters of the 20% solution. Then

50 - x

is the number of liters of the 60% solution. The total amount of acid in the final mixture is the sum of the amounts of acid from each solution. This can be written as the equation:

0.20x + 0.60(50 - x) = 0.30(50)

. Distribute on the left side:

0.20x + 30 - 0.60x = 15

. Combine the

x

terms:

-0.40x + 30 = 15

. Subtract 30 from both sides:

-0.40x = -15

. Divide by -0.40:

x = \frac{-15}{-0.40} = 37.5

. So, 37.5 liters of the 20% solution were used.