A laboratory technician prepares a cleaning solution by mixing a concentrated formula and … — GRE General Test

A laboratory technician prepares a cleaning solution by mixing a concentrated formula and distilled water in a ratio of $2 : 7$ by volume. If the technician uses $14$ liters of the concentrated formula, how many liters of distilled water are required?

A
$4$
B
$35$
$49$ Answer
D
$63$
E
$98$

Answer

49

liters of distilled water

The ratio of concentrated formula to distilled water is given as

2 : 7

. Since

14

liters of concentrated formula represents

2

ratio parts (

14 = 2 \times 7

), each ratio part equals

7

liters. Multiplying the

7

ratio parts of distilled water by

7

liters gives

7 \times 7 = 49

liters.

Step-by-Step Solution

Set up the proportion relating concentrated formula to distilled water

\frac{\text{Concentrated Formula}}{\text{Distilled Water}} = \frac{2}{7} = \frac{14}{x}

The given ratio is part-to-part (

2

parts formula for every

7

parts water).

Solve for the unknown volume

x

using cross-multiplication

2 \cdot x = 7 \cdot 14 \implies 2x = 98

Cross-multiplying equates the products of the diagonal terms in a proportion.

Divide by

2

to isolate

x

x = 49

Isolating

x

provides the required amount of distilled water in liters.

Key Concept

Direct Part-to-Part Proportions

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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