The sum of three numbers is 32. Twice the first minus the second is 11 less than the third. The third is the second minus three times the first. Find the numbers

Question

The sum of three numbers is 32. Twice the first minus the second is 11 less than the third. The third is the second minus three times the first. Find the numbers

Answer 1

2F - S = T-11

T= S - 3F

F+S+T = 32

3 equations, 3 unknowns, solve by elimination & substitution

S= T+3F,

F +T+3F +T = 32

4F +2T = 32

T=S-3F

T-11 = -S +2F add to eliminate S

2T -11 =-F

2T =11-F

4F + 11-F =32

3F = 21

F = 7

2T =11-7 = 4

T =2

S = 32 - 7 -2 = 23

First number = 7, second 23, third 2. They sum to 32

twice 1st - 2nd = 3rd - 11

2(7) - 23= 2-11

14-23 = -9

-9 =-9

3rd = 2nd - 3x1st

2 = 23-3(7) =23-21=2