Last year, amanda had $10,000 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 10% simple interest per year. after one year, she received a total of $760 in interest. how much did she invest in each account?

Let $x be invested in the account that paid 5% simple interest.
Let $y be invested in the account that paid 10% simple interest.

The total invested is $10,000, therefore
x + y = 10000            (1)

The interest amounts earned are respectively
x*1*0.06 = 0.06x
y*1*0.10 = 0.10y

The total interest earned is $760, therefore
0.06x + 0.10y = 760     
Multiply through by 10 to obtain
0.6x + y = 7600              (2)

Subtract (2) from (1).
x + y - (0.6x + y) = 10000 - 7600
0.4x = 2400
x = $6,000
From )1), obtain
y = 10000 - 6000 = $4,000

$6,000 in the account paying 6% simple interest, and
$4,000 in the account paying 10% simple interest.

Add up all the sides