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) (Show Source): You can put this solution on YOUR website!
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% = , or $
8E = 36(8,000) ----- Substituting 8,000 for S in eq (iii)
8E = 288,000
E, or amount invested at 8% = , or $
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 $
Im 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.
Send comments and thank-yous to D at MathMadEzy@aol.com
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