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

Answer:

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

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