A craft brewery blends two batches of cider. Batch A contains a 12\% sugar solution by vol… — GRE General Test

A craft brewery blends two batches of cider. Batch A contains a $12\%$ sugar solution by volume, and Batch B contains a $20\%$ sugar solution by volume. The brewer mixes $15$ liters of Batch A with $x$ liters of Batch B to create a resulting mixture that is $17\%$ sugar by volume. What is the value of $x$ ?

Answer: 25 liters

Answer

The value of

x

25

Equating the total amount of pure sugar before and after mixing gives

0.12(15) + 0.20x = 0.17(15 + x)

. Simplifying yields

1.8 + 0.20x = 2.55 + 0.17x

, which reduces to

0.03x = 0.75

, giving

x = 25

Step-by-Step Solution

Calculate the volume of pure sugar contributed by Batch A

0.12 \times 15 = 1.8

liters of pure sugar

Batch A is

12\%

sugar by volume and has a total volume of

15

liters.

Express the total volume of pure sugar in terms of

x

Total sugar volume =

1.8 + 0.20x

liters

Batch B adds

x

liters of a

20\%

sugar solution.

Set up the mixture equation

1.8 + 0.20x = 0.17(15 + x)

The final mixture has a total volume of

(15 + x)

liters with a concentration of

17\%

sugar.

Expand and solve the linear equation for

x

1.8 + 0.20x = 2.55 + 0.17x \implies 0.03x = 0.75 \implies x = 25

Subtract

0.17x

and

1.8

from both sides, then divide by

0.03

Key Concept

Linear Equations in One Variable (Mixture Word Problems)

Estimated Time:1m 30s

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