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

Algebra.Com
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 $

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.

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com

RELATED QUESTIONS

An investment of ​$130 comma 000 was made by a business club. The investment was split... (answered by ankor@dixie-net.com)
I have worked on this problem for three days, and need some help please. The question (answered by stanbon)
Please help me solve this equation: An investment of $50,000 was made by a business club. (answered by Theo)
An investment of ​$101 000 was made by a business club. The investment was split... (answered by advanced_Learner)
An investment of ​$92 comma 000 was made by a business club. The investment was... (answered by greenestamps)
An investment of ​$130 comma 000 was made by a business club. The investment was split... (answered by Theo)
An investment of ​$106,000 was made by a business club. The investment was split... (answered by mananth)
An investment of ​$70 comma 000 was made by a business club. The investment was split... (answered by mananth,MathTherapy)
An investment of $140,000 was made by a business club. The investment was split into... (answered by mananth)