Question

Dilbert invests a total of $31,000 in two accounts paying 4% and 10% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $2,260.00.

$_____was invested at 4%
$______was invested at 10%.

Answer 1

$14,000 was invested at 4%

$17,000 was invested at 10%

Explanation:

let x = the amount invested at 4%

y = the amount invested at 10%

from these, we can form an equation

x + y = 31,000 equation 1

and

4% of x plus 10% of y = 2,260

0.04x + 0.10y = 2,260 equation 2

let us multiply equation 2 by 100 to make it looks nice

4x + 10y = 226,000 equation 3

now, we can multiply equation 1 by -4

-4(x + y = 31,000)

-4x - 4y = -124,000 equation 4

add equations 3 and 4

4x + 10y = 226,000

-4x - 4y = -124,000

_________________

6y = 102,000

y = 17,000

substitute y = 17,000 to equation 1 to get c

x + y = 31,000

x + 17,000 = 31,000

x = 31,000 - 17,000

x = 14,000

Let's check if 4% of 14,000 plus 10% of 17,000 is equal to 2,260

(14,000 x 0.04) + (17,000 x 0.10) = 2,260

560 + 1,700 = 2,260