A barista has 40 ounces of a flavored drink mixture that is 30\% syrup by volume. How many… — GMAT

A barista has $40$ ounces of a flavored drink mixture that is $30\%$ syrup by volume. How many ounces of pure water must be added to reduce the syrup concentration to $24\%$ by volume?

Answer: 10 ounces

Answer

10 ounces of pure water must be added.

Adding 10 ounces of pure water increases the total volume of the mixture from 40 ounces to 50 ounces while keeping the volume of pure syrup constant at 12 ounces. The resulting concentration is 12 / 50 = 0.24, or 24% by volume.

Step-by-Step Solution

Calculate the volume of pure syrup present in the initial mixture

12

ounces of syrup

The initial 40-ounce mixture contains 30% syrup by volume (

40 \times 0.30 = 12

Set up the concentration equation after adding

x

ounces of pure water

\frac{12}{40 + x} = 0.24

Adding pure water increases the total volume to

40 + x

ounces without changing the amount of pure syrup.

Solve the linear equation for

x

x = 10

Multiplying both sides by

40 + x

yields

12 = 9.6 + 0.24x

, which simplifies to

2.4 = 0.24x

, giving

x = 10

Key Concept

Dilution of a mixture by adding pure solvent

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