Last year, Heather had $20,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she invested the rest in an account that paid 8% simple interest per year. After one year, she received a total of $1440 in interest. How much did she invest in each account?

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gomezmjosemiguel gomezmjosemiguel · Answer 1 · 2019-08-20T02:49:08+02:00

Answer:

The money invested in the account 1 was $8,000 and in the account 2 was 12,000.

Step-by-step explanation:

In this case we can formulate a system of equations that could find the amount invested in each account, this is:

Money invested in the account 1 is A

Money invested in the account 2 is B

Eq. 1: [tex]A+B=20,000[/tex]

Eq. 2: [tex]\frac{6}{100} *A+\frac{8}{100} *B=1,440[/tex]

Replacing the equation 1 in 2, this is:

[tex]\frac{6}{100} *(20,000-B)+\frac{8}{100} *B=1,440[/tex]

[tex]1,200-0.06B+0.08B=1,440[/tex]

[tex]0.02B=1,440-1,200[/tex]

[tex]B=\frac{240}{0.02}[/tex]

[tex]B=12,000[/tex]

Now, we can find A:

[tex]A=20,000-B[/tex]

[tex]A=20,000-12,000[/tex]

[tex]A=8,000[/tex]

The money invested in the account 1 was $8,000 and in the account 2 was 12,000.