SOLUTION: Twice my age plus three times my sister's age is 86. Three times my age plus four times my sister's age is 120. How old am I?

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Question 1154263: Twice my age plus three times my sister's age is 86. Three times my age plus four times my sister's age is 120. How old am I?

Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
let m = my age
let s = sister's age
:
Write an equation for each statement
:
twice my age plus three times my sister's age is 86.
2m + 3s = 86
Three times my age plus four times my sister's age is 120.
3m + 4s = 120
:
multiply the 1st equation by 3, the 2nd equation by 2
6m + 9s = 258
6m + 8s = 240
----------------subtraction eliminate m, find s
0 + s = 18 yr is sisters age
:
How old am I?
2m + 3(18) = 86
2m + 54 = 86
2m = 86 - 54
2m = 32
m = 32/2
m = 16 yr is my age
:
:
Check solutions in 2nd equation
3(16) + 4(18) =
48 + 72 = 120
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Twice my age plus three times my sister's age is 86. Three times my age plus four times my sister's age is 120. How old am I?
Let my age be M and my sister's, S

Then we get: 2M + 3S = 86 ------- eq (i)	

Also, 3M + 4S = 120 ------ eq (ii)	

M + S = 34 ----- Subtracting eq (i) from eq (ii)

S = 34 - M	

2M + 3(34 - M) = 86 ------ Substituting 34 - M for S in eq (i)

2M + 102 - 3M = 86

2M - 3M = 86 - 102

- M = - 16 

M, or my age is:  

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