Paige made $1411.75 last year by investing a total of $15,250 in two accounts: one paying 8.5% annual interest and the other paying 10% annual interest. how much did she invest in each account?

Lets x and y are 2 accounts Paige invested
x account invested with annual interest rate 8.5%
y account invested with annual interest rate 10%

x + y =15,250 so x = 15,250 - y
0.085x + 0.1y = 1,411.75

substitute x = 15,250 - y into 0.085x + 0.1y = 1,411.75

0.085x + 0.1y = 1411.75
0.085(15,250 - y) + 0.1y = 1,411.75
1,296.25 - 0.085y + 0.1y = 1,411.75
0.015y = 115.5
y = 7,700

x = 15,250 - y
x = x = 15,250 - 7,700
x = 7,550

answer

$7,550 invested on account with annual interest rate 8.5%
$7,700 invested on account with annual interest rate 10%