An investor divides a total of \15,000 between two accounts, Account P and Account Q. Acco… — GRE General Test

An investor divides a total of $\$15,000$ between two accounts, Account P and Account Q. Account P earns an annual simple interest rate of $6\%$ , while Account Q earns an annual simple interest rate of $8\%$ . If the total interest earned from both accounts combined after one year is $\$1,020$ , how much more money was invested in Account P than in Account Q?

A
$\$1,500$
$\$3,000$ Cevap
C
$\$4,500$
D
$\$6,000$
E
$\$9,000$

Cevap

\$3,000

Setting up the system of linear equations

p + q = 15,000

and

0.06p + 0.08q = 1,020

yields

p = 9,000

and

q = 6,000

. Subtracting the amount in Account Q from Account P gives

9,000 - 6,000 = 3,000

. Thus,

\$3,000

is the correct answer.

Adım Adım Çözüm

Define variables and set up the system of linear equations

Let

p

be the amount invested in Account P and

q

be the amount invested in Account Q. The equations are

p + q = 15,000

and

0.06p + 0.08q = 1,020

The first equation represents the total investment amount, and the second equation represents the total annual interest earned.

Simplify the interest equation and solve for one variable using elimination

Multiply

0.06p + 0.08q = 1,020

by 100 to obtain

6p + 8q = 102,000

, which simplifies to

3p + 4q = 51,000

. Multiplying the first equation by 3 yields

3p + 3q = 45,000

. Subtracting this from

3p + 4q = 51,000

gives

q = 6,000

Eliminating

p

allows for direct calculation of the amount invested in Account Q.

Calculate the amount invested in Account P

p = 15,000 - 6,000 = 9,000

Substitute the value of

q

back into the total investment equation.

Determine the requested difference

p - q = 9,000 - 6,000 = 3,000

The question specifically asks how much more money was invested in Account P than in Account Q.

Anahtar Kavram

Solving Systems of 2x2 Linear Equations for Word Problems

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Adım Adım Çözüm

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