Question

A business woman invests $41,500 into two accounts: one that returns 8% annual interest and one that returns 15% annual interest. After 1 year, she earns $5490. How much did she invest in each account?

$10,500 in the 8% interest account, $31,000 in the 15% interest account.

$11,500 in the 8% interest account, $30,000 in the 15% interest account.

$9,500 in the 8% interest account, $32,000 in the 15% interest account.

$32,000 in the 8% interest account, $9,500 in the 15% interest account.

Answer 1

$10,500 in the 8% interest account,

$31,000 in the 15% interest account

Explanation:

Let

x ---> the amount invested in the 8% interest account

41,500-x ----> the amount invested in the 15% interest account

we know that

The amount invested in the 8% interest account multiplied by the interest in decimal form plus the amount invested in the 15% interest account multiplied by the interest in decimal form, must be equal to $5,490

so

The linear equation that represent this problem is

`0.08x+0.15(41,500-x)=5,490`

solve for x

`0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500`

so

`41,500-x=41,500-10,500=\$31,000`

therefore

$10,500 in the 8% interest account,

$31,000 in the 15% interest account