A laboratory technician has 12 liters of a solution containing 15\% salt by weight. The te… — GRE General Test

A laboratory technician has $12$ liters of a solution containing $15\%$ salt by weight. The technician wants to increase the salt concentration to $25\%$ by adding a second solution that contains $40\%$ salt by weight. How many liters of the $40\%$ solution must be added?

Cevap: 8 liters

Cevap

8 liters of the 40% solution must be added.

The total amount of salt contributed by the two solutions is

0.15(12) + 0.40x = 1.8 + 0.40x

. The final mixture volume is

(12 + x)

liters, and its concentration must be

25\%

. Equating the total salt to

25\%

of total volume yields

1.8 + 0.40x = 0.25(12 + x)

. Expanding gives

1.8 + 0.40x = 3.0 + 0.25x

, which simplifies to

0.15x = 1.2

, giving

x = 8

liters.

Adım Adım Çözüm

Define the unknown variable and calculate the initial solute quantity.

Let

x

be the volume of the

40\%

solution added (in liters). Salt in initial solution =

0.15 \times 12 = 1.8

liters.

Establishing the mass balance of the salt solute is necessary to construct the algebraic equation.

Set up the algebraic concentration equation.

1.8 + 0.40x = 0.25(12 + x)

The combined salt from both solutions must equal

25\%

of the total combined liquid volume

(12 + x)

liters.

Solve the linear equation for

x

1.8 + 0.40x = 3.0 + 0.25x \implies 0.15x = 1.2 \implies x = 8

Isolating

x

yields the exact number of liters required.

Anahtar Kavram

Algebraic mixture problems using mass balance equations.

Tahmini Süre:1m 30s

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