SOLUTION: An investment of ​$92 comma 000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned&#820

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Question 1130191: An investment of ​$92 comma 000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned​ 8% interest, the second​ 6%, and the third​ 9%. Total interest from the investments was $ 7200.  The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment.
Answer by greenestamps(13200) About Me  (Show Source):
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The amount of interest from the part at 8% was 4 times the amount of interest from the part at 6%. The 8% rate is 4/3 of the 6% rate; to get 4 times as much interest, using an interest rate that is 4/3 as large, the amount at 8% must be 3 times the amount at 6%. So

let x = amount at 6%
then 3x = amount at 8%
and (92000-4x) = amount at 9%

The total interest was $7200:

.06%28x%29%2B.08%283x%29%2B.09%2892000-4x%29+=+7200
.06x%2B.24x%2B8280-.36x+=+7200
1080+=+.06x
x+=+1080%2F.06+=+18000

ANSWER: The amounts invested at each rate were

6%: x = $18000
8%: 3x = $54000
9%: $92000-4x = $20000

CHECK: .06%2818000%29%2B.08%2854000%29%2B.09%2820000%29+=+1080%2B4320%2B1800+=+7200