I need help with a math problem :(?

Question

I am in an independent study class and have several problems like this one but I cant seem to figure it out. Once I get it down to an equation with 2 variables I get stuck. I can get an equation that I can substitute for one variable but it is not working out. What am I doing wrong? I included the problem below and my work.

Phil has $20,000, part of which he invests at 8% interest and the rest at 6%. If his total interest from the 2 investments is $1460, how much is invested at each rate.

.08x + .06y =1460

.08x=1460-.06y

.08x/.08= (1460-.06y)/.08

x=18250-.75y

.08(18250-.75y)+.06y=1460

1460-.06y+.06y=1460

1460=1460

WTF? I apparently have no idea how to do this. This problem was given to me in a packet of papers with no real directions or sample problems. Any help that you can give me is really appreciated. I do know the answers, but I have no idea how to get there.

The amounts invested are $13000 and $7000.

Answer 1

Let x be the amount invested at 6%.

Let 20,000-x be the amount invested at 8%.

0.06x + 0.08*(20,000-x) = 1460

1600 - 0.02x = 1460

x = $7,000

20,000-x = $13,000

  

Answer 2

Your equation, .08x + .06y = 1460, is correct, but to solve the problem you need to also make a second equation. The problem says he invests part at 8% interest, and the rest at 6% interest, so if x is the amount he invests at 8% and y is the amount at 6%, then x + y = 20000, right?

You rearranged the equation to get x=18250 - .75y. Substitute for x in the second equation, and you'll get

(18250 - .75y) + y = 20000

18250 + .25y = 20000

.25y = 1750

.25y/.25 = 1750/.25

y = 7000

Now solve for x by substituting this y value into one of the equations:

x+y = 20000

x + (7000) = 20000

x = 130000

So you get your answers, $13000 at 8% and $7000 at 6%.

Answer 3

You need 2 different equations with x and y otherwise you can't solve the problem.

What you do is solve the first equation for x as you already did

x=18250-.75y

then you substitute X in the second equation for 18250-.75y and solve for y. once you know y you plug that back in and get x.

You can't sub x back into the same equation otherwise you get nothing like you just discovered.

try coming up with a second equation relating x and y together then its easy.

Answer 4

the first equation is true:

.08x + .06y =1460

the second equation:

x+y=20000

4x+3y=73000

3x+3y=60000

x=13000

y=20000-13000=7000