A student takes out two loans to help pay for college expenses. The total amount of money borrowed is $8050. Both loans have interest that accrues annually. The first loan has an interest rate of 8.5%, and the second loan has an interest rate of 2.5%. After the first year, the interest from both loans total $297.25. Find the initial amount borrowed at 2.5%. Round to the nearest dollar.

Question

A student takes out two loans to help pay for college expenses. The total amount of money borrowed is $8050. Both loans have interest that accrues annually. The first loan has an interest rate of 8.5%, and the second loan has an interest rate of 2.5%. After the first year, the interest from both loans total $297.25. Find the initial amount borrowed at 2.5%. Round to the nearest dollar.
Amount at 2.5%: 
can you please check my answer..thanks
is it
$ 6.450.00

oobleck · Answer

If $x at 2.5%, then 0.025x + 0.085(8050-x) = 297.25 so your answer looks good

mathhelper · Answer

amount borrowed at 8.5% --- x
amount borrowed at 2.5% ---- 8050-x

.085x + .025(8050-x) = 297.25
times 1000
85x + 25(8050-x) = 297250
85x + 201250 - 25x = 297250
60x = 96000
x = 1600

amount borrowed at 8.5% = $1600
amount borrowed at 2.5% = 8050 - 1600 = 6450