SOLUTION: The sum of three numbers is 32. Twice the first minus the second is 5 less than the third. The third is the second minus three times the first. Find the numbers.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The sum of three numbers is 32. Twice the first minus the second is 5 less than the third. The third is the second minus three times the first. Find the numbers.      Log On


   

Question 1185610: The sum of three numbers is 32. Twice the first minus the second is 5 less than the third. The third is the second minus three times the first. Find the numbers.
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 32. Twice the first minus the second is 5 less than the third. The third is the second minus three times the first. Find the numbers.
=========================
F + S + T = 32
2F - S = T - 5
T = S - 3F
-----
Sub for T in the 1st 2 equations.
---
F + S + S - 3F = 32
-2F + 2S = 32 ---> F - S = -16 ---> F = S-16
----
2F - S = S - 3F - 5 ---> 5F - 2S = -5
----
F = S-16
5F - 2S = -5
Sub for F
5(S-16) - 2S = -5
3S - 80 = -5
S = 25
============
F = 9
T = -2
9, 25, -2 are the 3 numbers in order

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x,y,z; first, second, third

system%28x%2By%2Bz=32%2C2x-y=z-5%2Cz=y-3x%29

From E2 and E3
system%28z=2x-y%2B5%2Cz=-3x%2By%29
Equating expressions for z
2x-y%2B5=-3x%2By
5x-2y=-5

Using E3 to substitute into E1
x%2By%2By-3x=32
-2x%2B2y=32
-x%2By=16

Revising the system in two variables:
system%285x-2y=-5%2C-x%2By=16%29


That still could be shown as
system%285x-2y=-5%2C-2x%2B2y=32%29
Add:
3x=27
highlight_green%28x=9%29
From that, you can solve for y and z.