SOLUTION: System of linear equations word problem. Help please! An Investment of 54,000 was made by a club. It was split into three parts lasting only year. The first part of the investme

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Question 636217: System of linear equations word problem. Help please!
An Investment of 54,000 was made by a club. It was split into three parts lasting only year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from investments was $4260. The interest from the first was 6 times from the second. Find the amounts of the three parts of the investments.
Answer by MathTherapy(10552) About Me  (Show Source):
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System of linear equations word problem. Help please!
An Investment of 54,000 was made by a club. It was split into three parts lasting only year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from investments was $4260. The interest from the first was 6 times from the second. Find the amounts of the three parts of the investments.

Let the amounts invested at 8%, 6%, and 9% be E, S, and N, respectively
Forming equations based on info provided, we have:
E + S + N = 54,000 ------ eq (i)

.08E + .06S + .09N = 4,260
8E + 6S + 9N = 426,000 ---- Multiplying by 100 ------ eq (ii)

.08E = 6(.06S) ----- .08E = .36S
8E = 36S ---- Multiplying by 100 ------ eq (iii)

36S + 6S + 9N = 426,000 ------ Substituting 36S for 8E in eq (ii)
42S + 9N = 426,000 ------ eq (iv)

– 8E – 8S – 8N = - 432,000 ----- Multiplying eq (i) by – 8 ----- eq (v)
8E + 6S + 9N = 426,000 ----- eq (ii)
– 2S + N = - 6,000 ----- Adding eqs (v) & (ii) ----- eq (vi)

42S + 9N = 426,000 ----- eq (iv)
18S – 9N = 54,000 ------- Multiplying eq (vi) by – 9 ----- eq (vii)
60S = 480,000 ------ Adding eqs (iv) & (vii)
S, or amount invested at 6% = 480000%2F60, or $highlight_green%288000%29

8E = 36(8,000) ----- Substituting 8,000 for S in eq (iii)
8E = 288,000
E, or amount invested at 8% = 288000%2F8, or $highlight_green%2836000%29

36,000 + 8,000 + N = 54,000 ----- Substituting 8,000 for S, and 36,000 for E in eq (i)
44,000 + N = 54,000
N, or amount invested at 9% = 54,000 – 44,000, or $highlight_green%2810000%29

I’m sure you can do your own check!!

If you know and are more comfortable with matrices, you could also determine the three unknown amounts using this method.

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