I have a math question

Question

Last year, Amy had $20,000 to invest. She invested some of it in an account that paid 7% 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 $1590 in interest. How much did she invest in each account?

First account: $

Second account: $

Answer 1

.08x + .07(20,000-x) = 1590

.08-.07x = 1590 -.07(20,000)

.01x = 1590 - 1400

.01x = 190

x = $19,000 invested at 8%

20,000-19000 = $1,000 invested at 7%

.08(19000) + .07(1000)

= 1520 +700

=1590

1590/20000

=159/2000

=.0795=7.95% average interest

7 is within .95 of 7.95

8 is within .05 of 7.95

95/5 = 19

amount invested at 8% should be 19 times as much as invested at 7%

$19,000 invested at 8%

$1,000 invested at 7%

19000/1000 = 19