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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.

Respuesta :

calculista

Answer:

$10,500 in the 8% interest account,

$31,000 in the 15% interest account

Step-by-step 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

[tex]0.08x+0.15(41,500-x)=5,490[/tex]

solve for x

[tex]0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500[/tex]

so

[tex]41,500-x=41,500-10,500=\$31,000[/tex]

therefore

$10,500 in the 8% interest account,

$31,000 in the 15% interest account

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