Answer:
- $70,000 at 7%
- $304,000 at 8%
Step-by-step explanation:
<u>Given</u>:
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%.
<u>Find</u>:
The amount invested at each rate.
<u>Solution</u>:
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%.
<u><em>Check</em></u>
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
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<em>Comment on 6-step method</em>
We have tried to hit the highlights. Your steps appear to be ...
- Identify the given information (Given)
- Identify the question you are asked to answer (Find)
- Identify the useless information in the problem statement (is none)
- Decide on a strategy. Make a model or drawing. (model equation shown)
- Solve and show work (Solution)
- Explain why the answer makes sense (Check)
