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.

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) (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.
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F + S + T = 32
2F - S = T - 5
T = S - 3F
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Sub for T in the 1st 2 equations.
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F + S + S - 3F = 32
-2F + 2S = 32 ---> F - S = -16 ---> F = S-16
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2F - S = S - 3F - 5 ---> 5F - 2S = -5
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F = S-16
5F - 2S = -5
Sub for F
5(S-16) - 2S = -5
3S - 80 = -5
S = 25
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F = 9
T = -2
9, 25, -2 are the 3 numbers in order
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x,y,z; first, second, third

From E2 and E3

Equating expressions for z

Using E3 to substitute into E1

Revising the system in two variables:

That still could be shown as

Add:

From that, you can solve for y and z.
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