SOLUTION: The sum of three numbers is 16. Twice the smallest is 2 less than the largest, and the sum of the largest and smallest is 11. Use a linear system in three variables to find the thr

Algebra ->  Finance -> SOLUTION: The sum of three numbers is 16. Twice the smallest is 2 less than the largest, and the sum of the largest and smallest is 11. Use a linear system in three variables to find the thr      Log On


   

Question 1021455: The sum of three numbers is 16. Twice the smallest is 2 less than the largest, and the sum of the largest and smallest is 11. Use a linear system in three variables to find the three numbers. (Enter solutions from smallest to largest.)
Found 2 solutions by Fombitz, josgarithmetic:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.A%2BB%2BC=16
2.2A=C-2
3.A%2BC=11
Substitute 3 into 1,
11%2BB=16
B=5
Then from eq. 2,
C=2A%2B2
Substitute into eq. 3,
A%2B2A%2B2=11
3A=9
A=3
and from eq. 3,
3%2BC=11
C=8
3,5,8

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%3Cy%3Cz

system%28x%2By%2Bz=16%2C2x=z-2%2Cx%2Bz=11%29

system%28x%2By%2Bz=16%2C2x-z=0%2Cx%2Bz=11%29

First and last equations will allow for elimination method to quickly find y.
%28x%2By%2Bz%29-%28x%2Bz%29=16-11
highlight%28y=5%29

A simpler system just using last two equations lets you solve for x and z.
system%282x-z=0%2Cx%2Bz=11%29
Add corresponding members will eliminate z...
2x-z%2Bx%2Bz=11
3x=11
highlight%28x=11%2F3%29

YOU can finish, finding z.