SOLUTION: An executive invests $25,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $1,780, how much is invested at each rate?
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Question 1121631: An executive invests $25,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $1,780, how much is invested at each rate? Answer by ikleyn(52781) (Show Source):
Let x be an amount invested at 8%, in dollars.
Then the amount invested at 6% was (25000-x) dollars.
Your equation is
interest + interest = total interest
0.08*x + 0.06*(25000-x) = 1780 dollars.
Simplify and solve for x:
0.08x + 0.06*25000 - 0.06x = 1780
0.02x = 1780 - 0.06*2500 = 280 ====> x = = 14000.
Answer. $14000 was invested at 8%. The rest $25000 - $14000 = $11000 was invested at 6%.
Check. 0.08*14000 + 0.06*11000 = 1780 dollars. ! Correct !
Solved.
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It is a typical and standard problem on investment.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
