Question

Set up and solve a system of equations to solve the problem.

Helene invested a total of $1,000 in two simple-interest bank accounts. One account paid 5% annual interest; the other paid 7% annual interest. The total amount of interest she earned after 1 year was $62. Find the amount invested in each account.
Helene invested $_ in the 5% interest account and $_ in the 7% account.

Answer 1

Helene invested $400 in the 5% account and $600 in the 7% account.

Explanation:

Let x and y represent the amounts Helene invested in the 7% and 5% accounts, respectively. Then a system of equations based on the problem statement can be ...

x + y = 1000

0.07x +0.05y = 62

Solving the first equation for y and substituting that into the second equation, we get ...

y = 1000 -x . . . . . . subtract x from both sides of the first equation

0.07x +0.05(1000 -x) = 62 . . . after substitution for y

0.02x + 50 = 62 . . . . . . . . . simplify

0.02x = 12 . . . . . . . . . . . . . . subtract 50

12/0.02 = x = 600 . . . . . . . .divide by the coefficient of x

y = 1000 -x = 1000 -600

y = 400

Helene invested $400 in the 5% account and $600 in the 7% account.