Three equation systems with a missing variable in only one system?

Question

An investment of 130,000 is made by a business club. The investment is split in three parts and it lasted for one year. The first part of the investment earned .8%, the second .6% and the third .9%. Total interest from the investment was $9540. The interest was 2 times the intrest from the second. Find all three amounts of the investment.

---------------------

I know how to set up the sytem from there. I have:

130,000=x+y+z
9540=.08x+.06y+.09z
x = 2y

On the second equation, I times all of the terms by 100 so that I got rid of the decimals. So now I have:

130,000=x+y+z
954000=8x+6y+9z
x = 2y

I know you're supposed to solve it and what not, but I guess what I am asking is how do you do it? Do you plug in x =2y for both of first and second equations and figure it out from there? Or do you eliminate the z's and then solve?

I'm asking because I keep getting decimals and my math professor told me that I should not have any decimals or fractions.

Solving this with how you did would be very helpful. Thank you!

Battleaxe · Accepted Answer

I think you made an error in writing the third equation. I think it meant that the total interest is twice that of the interest on the second amount.
1) x + y + z = 130,000
2) 0.08x + 0.06x + 0.09z = 9540
3) 9540 = 2(0.06y)
Solving eq(3) and substituting into eqs(1) and(2) will give two equations and two unknowns.

- .--

Paula · Answer

You percentages are out by a factor of 10. Your second line should be:

9540 = .008x + .006y + .009z

Also if you've typed it correctly, "The interest was 2 times the intrest from the second" then to me that means the total interest was 2 times what was earned from the second, i,,e,

9540 = 2(0.006y)

I haven't gone through the arithmetic but does that help?

EDIT: Whoah! I've just had another look and something is badly wrong with this question, at least how you typed it. The total net interest (total gain divided by intial total) is 7.34% ! Were the interests earned mean to be whole numbers? i.e. 8%, 6% and 9%? If that is the case then your second equation is correct but your 3rd should read:
9540 = 2(0.06y)
which gives:
y = 9540 / 0.12 = 79500
and then hopefully you can get x and z from there...

Trending News

Three equation systems with a missing variable in only one system?

2 Answers