A cleaning mixture is prepared by combining bleach and water in a ratio of 1:8. If a conta… — ACT

A cleaning mixture is prepared by combining bleach and water in a ratio of $1:8$ . If a container holds a total of $36$ cups of this mixture, how many cups of bleach were used?

A
$4.5$
B
$8$
$4$ Answer
D
$32$
E
$28$

Answer

4 cups

The correct answer is 4. The ratio of bleach to water is

1:8

, which means the entire mixture is divided into

1 + 8 = 9

equal parts. Bleach constitutes

\frac{1}{9}

of the overall mixture. By taking

\frac{1}{9}

of the

36

-cup total volume, we find that the amount of bleach used is

4

cups.

Step-by-Step Solution

Determine the total parts in the mixture's ratio.

1 + 8 = 9

total parts

Since the ratio of bleach to water is

1:8

, the mixture is composed of

1

part bleach for every

8

parts water.

Express the bleach portion as a fraction of the total mixture.

\frac{1}{9}

The bleach represents

1

part out of the

9

total parts in the mixture.

Find the amount of bleach in the

36

-cup container.

\frac{1}{9} \times 36 = 4

cups

Multiply the fraction of bleach by the total volume of the cleaning mixture.

Key Concept

Determining a part from a part-to-part ratio and a total quantity

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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