A technician at a chemistry lab prepares a solution by mixing 3 milliliters of acid with e… — SAT

A technician at a chemistry lab prepares a solution by mixing $3$ milliliters of acid with every $7$ milliliters of distilled water. If the technician uses $35$ milliliters of distilled water to prepare the solution, how many milliliters of acid are needed?

Answer: 15 milliliters

Answer

The correct answer is 15.

To maintain the ratio of

3

milliliters of acid for every

7

milliliters of distilled water, the proportion

\frac{\text{acid}}{\text{water}} = \frac{3}{7} = \frac{x}{35}

is established. Multiplying both sides by

35

gives

x = 35 \times \frac{3}{7} = 15

milliliters of acid.

Step-by-Step Solution

Set up the proportion relating acid to distilled water.

\frac{3}{7} = \frac{x}{35}

, where

x

is the required amount of acid in milliliters.

The ratio of acid to distilled water must remain constant.

Solve the proportion for

x

x = 15

Multiply both sides of the equation by 35 to isolate

x

Key Concept

Solving proportions to find an unknown quantity when the ratio is constant.

Alternative Method

Find the scale factor:

35

divided by

7

5

. Multiply the acid amount (

3

) by this scale factor of

5

to get

15

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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