Question

Juan invests a total of $20,500 in two accounts paying 15% and 6% simple interest, respectively. How much was invested in each account if, after one year, the total interest was $2,220.00.

A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use x as your variable to represent the amount of money invested in the account paying 15% simple interest.

Answer 1

$11,000 was invested at 15%

$9,500 was invested at 6%

Explanation:

let x = the amount invested at 15%

y = the amount invested at 6%

from these, we can form an equation

x + y = 20,500 equation 1

and

15% of x plus 6% of y = 2,220

0.15x + 0.06y = 2,220 equation 2

let us multiply equation 2 by 100

15x + 6y = 222,000 equation 3

now, we can multiply equation 1 by -15

-15(x + y = 20,500)

-15x - 15y = -307,500 equation 4

add equations 3 and 4

15x + 6y = 222,000

-15x - 15y = -307,500

________________

-9y = -85,500

y = 9,500

substitute y = 9,500 to equation 1 to get x

x + y = 20,500

x + 9,500 = 20,500

x = 20,500 - 9,500

x = 11,000

Let's check if 15% of 11,000 plus 6% of 9,500 is equal to 2,220

(11,000 x 0.15) + (9,500 x 0.06) = 2,220

1,650 + 570 = 2,220