Question

Billy invested $18 dollars of savings in two major business enterprises which paid interest at the rate of 3% and 6%, respectively. If his annual income for these two enterprises was equivalent to a return of 5% on the entire investment, find how much he invested at 3%.

Answer 1

Let the amount invested at 3% = x
Let the amount invested at 6% = y.
From the total amount invested, we get this equation.
x + y = 18

Now we look at the interest earned.
The 3% account earns 0.03x
The 6% account earns 0.06y
5% on the entire amount is 0.05 * 18 = 0.9
This gives us the second equation.

0.03x + 0.06y = 0.9


Now we have a system of 2 equations in 2 unknowns.

x + y = 18
0.03x + 0.06y = 0.9

Solve the first equation for y:
y = 18 - x

Replace 18 - x for y in the second equation.

0.03x + 0.06y = 0.9

0.03x + 0.06(18 - x) = 0.9

0.03x + 1.08 - 0.06x = 0.9
-0.03x + 1.08 = 0.9
-0.03x = -0.18
x = 6

Answer: He invested $6 at 3%.