Question

An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the investment is $29220. How much
did he invest at each amount? Use the six-step method.

He invested $_____at 7% and ____at 8%.

Answer 1

Answer:

• $70,000 at 7%
• $304,000 at 8%

Step-by-step explanation:

Given:

  Total interest earned on two investments is $29,220.

  An amount is invested at 7%.

  $24,000 more than 4 times that amount is invested at 8%.

Find:

  The amount invested at each rate.

Solution:

  Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

  interest on 7% account + interest on 8% account = total interest

  0.07x + 0.08(24000+4x) = 29220

  0.39x + 1920 = 29220 . . . . . . . . . . . simplify

  0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

  x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

  24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

  7% interest + 8% interest = 29,220

  0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

Comment on 6-step method

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1. Identify the given information (Given)
2. Identify the question you are asked to answer (Find)
3. Identify the useless information in the problem statement (is none)
4. Decide on a strategy. Make a model or drawing. (model equation shown)
5. Solve and show work (Solution)
6. Explain why the answer makes sense (Check)