SOLUTION: If two times Sam’s age plus three times Sarah’s age equals 34 and Sarah’s age is also five times Sams age how old is Sarah

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Question 1132193: If two times Sam’s age plus three times Sarah’s age equals 34 and Sarah’s age is also five times Sams age how old is Sarah

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
system%282y%2B3x=34%2Cx=5y%29

system%283x%2B2y=34%2Cx-5y=0%29

system%2815x%2B10y=170%2C2x-10y=0%29

17x=170

highlight%28x=10%29-----------Sarah

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A solution using two equations with two unknowns, solved by substitution, is of course valid; but it is far more work than necessary for this problem.

Since one of the pieces of given information is that Sarah is 5 times as old as Sam, it is easy to set up a solution using only one unknown:

let x = Sam's age
then 5x = Sarah's age

2 times Sam's age plus 3 times Sarah's age equals 34:

2%28x%29%2B3%285x%29+=+34
17x+=+34
x+=+2

ANSWER: Sarah's age is 5x = 10.