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An executive invests $30,000, some at 10% and some at 5%. If she receives an annual return of $2,200, how much is invested at 10%?
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1. Solution with two unknowns
Let t be an amount invested at 10%, and f be an amount invested at 5%. Then you have these to equations
t + f = 30000,
0.1t + 0.05f = 2200.
You can solve it by the substitution method or by the elimination method.
2. Solution with one unknown
Then your equation is
0.1t + 0.05*(30000-t) = 2200, or
0.1t + 5*300 - 0.05t = 2200, or
0.05t = 2200-1500, or
0.05t = 700, t = = 14000.
Answer. 14000 invested at 10%, 16000 invested at 5%.