Last year, Sung had $20,000 to invest.

Question

Last year, Sung had
$20,000
to invest. He invested some of it in an account that paid
10%
simple interest per year, and he invested the rest in an account that paid
6%
simple interest per year. After one year, he received a total of
$1400
in interest. How much did he invest in each account?

Answer 1

Sung invested $ 20,000 in two accounts.  Let one account be x, another account be y.

x + y = 20,000 --------------- Equation 1

 

One account paid 10% interest and another paid 6%.  Total interest received was $1400

0.1 x + 0.06 y = 1400 -------------Equation 2.

 

Now there are two variables in two equations that can be solved by substitution or by elimination method.

 

To solve by substitution, first isolate x in the first equation by subtracting y on both sides.

 

x + y = 20,000

x + y - y = 20,000 - y

x = 20,000 - y

 

Now substitute x = 20,000 - y into  equation 2.

 

0.1 x + 0.06 y = 1400

0.1 ( 20,000 - y ) + 0.06 y = 1400 ---------------  Distribute and combine like terms

2000 - 0.1 y + 0.06 y = 1400

- 0.04 y = - 600 ---------- subtract both sides by - 0.04

- 0.04 y/ -0.04 = -600/ -0.04

y = 15,000

 

Substitute y = 15,000 in to equation 1 and solve for x.

 

x + y = 20,000

x + 15,000 = 20,000

x = 5000.

 

$5,000 was invested at 10% and $15,000 was invested at 6%.