SOLUTION: the sum of three numbers is 39. the sum of the first and second is twice the third. the sum of the second and the third is 3 more than twice the first. find the third number

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Question 956656: the sum of three numbers is 39. the sum of the first and second is twice the third. the sum of the second and the third is 3 more than twice the first. find the third number
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y+Z=39
X+Y=2Z
Y+Z=2X+3
REPLACE (X+Y) WITH 2Z IN THE FIRST EQUATION
2Z+Z=39
3Z=39
Z=39/3
Z=13 ANS.
X+Y+13=39
X+Y=39-13
X+Y=26
Y+13=2X+3
Y-2X=3-13
Y-2X=-10
Y=2X-10
REPLACE Y WITH 2X-10 & SOLVE FOR X
X+(2X-10)=26
3X=26+10
3X=36
X=36/3
X=12 ANS.
Y=2*12-10=24-10=14 ANS.
PROOF:
12+14+13=39