Question

In one year, Michael earned $6300 as a work study in college. He invested part of the money at 9% and the rest at 7%. If he received a total of $493 in interest at the end of the year, how much was invested at 7%? How much was invested 9%?

Answer 1

He invested x at 9% and y at 7%.
The total investment was $6300, so
x + y = 6300

The 9% account earned 0.09x in interest.
The 7% account earned 0.07y in interest.
The total interest earned was
0.09x + 0.07y = 493

We have 2 equations in 2 unknowns. We solve the equations as a system of equations.

Solve the first equation for x and substitute in the second equation.

x = 6300 - y

0.09(6300 - y) + 0.07y = 493

567 - 0.09y + 0.07y = 493

-0.02y = -74

y = 3700

x + y = 6300

x + 3700 = 6300

x = 2600

He invested $2600 at 9% and 3700 at 7%