Pre calc question

Question

A bank loaned out $3700, part of it at a rate of 7.1% per year and the rest of it at a rate of 5.6% per year. The total amount of interest owed to the bank at the end of one year was $252.99.

Find the amount of money that the bank loaned out at 7.1%.

Round your answer to the nearest cent (2 places after the decimal point), and do NOT type a dollar sign in the answer box.

Amount of money loaned at 7.1%: $

Answer 1

.071x + .056(3700-x)= 252.99

.071x -.056x = 252.99 - .056(3700)

.015x = 252.99- 207.2= 45.79

x = 45.79/.015 = $3,052.67 invested at 7.1%

3700-3052.67 = $647.33 invested at 5.6%

check the answers

.071(3052.67) + .056(647.33)

=216.74 + 36.25

= 252.99