linear equations

Question

Last year, Latoya had
$10,000
to invest. She invested some of it in an account that paid
8%
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
$860
in interest. How much did she invest in each account?

Answer 1

The trick in this equation is trying to figure out how to set the problem up in the first place:

x + y = 10,000 (x and y are the amounts invested into the two separate accounts)

.08x + .1y = 860  (8% of one and 10% of the other made $860)

 

Now, we can solve via substitution by moving one of the variable in the first equation to the right side, or we can try elimination by multiplying the second equation by -10 and get rid of that y. I think we'll go with substitution in this case:

y = 10,000 - x

 

.08x + .1(10,000 - x) = 860

.08x + 1,000 - .1x = 860

-.02x + 1,000 = 860

-.02x = -140

x = 7000

 

y = 10000 - 7000

y = 3000

 

Now to check the answer:

.08 * 7000 + .1 * 3000 = 860

560 + 300 = 860

860 = 860