A chemist mixes x ounces of a 40% acid solution with y ounces of a 70% acid solution to pr… — GRE General Test

A chemist mixes $x$ ounces of a 40% acid solution with $y$ ounces of a 70% acid solution to produce a 20-ounce mixture that is 52% acid. What is the value of $x - y$ ?

A
-4
4Cevap
C
8
D
12
E
20

Cevap

Setting up the linear system

x + y = 20

and

0.40x + 0.70y = 10.4

leads to

x = 12

and

y = 8

. Subtracting

y

from

x

yields

12 - 8 = 4

Adım Adım Çözüm

Set up the system of linear equations based on total solution volume and pure acid content.

Total volume equation:

x + y = 20

. Pure acid equation:

0.40x + 0.70y = 0.52(20) = 10.4

The sum of the component volumes equals the total volume, and the sum of the pure acid contents equals the total acid content.

Multiply the acid equation by 10 to eliminate decimals.

4x + 7y = 104

Clearing decimals simplifies the subsequent elimination calculation.

Solve for

y

using the elimination method.

Multiply

x + y = 20

by 4 to get

4x + 4y = 80

. Subtract this from

4x + 7y = 104

(4x + 7y) - (4x + 4y) = 104 - 80 \implies 3y = 24 \implies y = 8

Eliminating the variable

x

isolates

y

Solve for

x

and compute

x - y

x = 20 - 8 = 12

. Therefore,

x - y = 12 - 8 = 4

Substitute

y = 8

back into the first equation and calculate the requested expression.

Anahtar Kavram

Systems of Linear Equations in Mixture Problems

Soru

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