Answer:
- $70,000 at 7%
- $304,000 at 8%
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
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