SOLUTION: The sum of Ellen’s and Todd’s ages is 34 years. Five years ago, the sum of twice Ellen’s age and three times Todd’s age was 61 years. How old are they now?

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Question 1176141: The sum of Ellen’s and Todd’s ages is 34 years. Five years ago, the sum of twice Ellen’s age and three times
Todd’s age was 61 years. How old are they now?

Found 2 solutions by CubeyThePenguin, MathLover1:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
E = Ellen's age
T = Todd's age

E + T = 34
2(E-5) + 3(T-5) = 61

E + T = 34
2E + 3T = 61+25 = 86

Multiply the first equation by 3:

3E + 3T = 102
2E + 3T = 86

Subtract to get E = 16 and T = 18.

Ellen is 16 and Todd is 18.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let' Ellen’s age be E and Todd’s age T
if the sum of Ellen’s and Todd’s ages is 34+years, we have
E%2BT=34.......solve for E
E=34-T.........eq.1
if five years ago, the sum of twice Ellen’s age and three+times
Todd’s age was 61 years,
2%28E-5%29%2B3%28T-5%29=61.......eq.2........substitute E from eq.1
2%2834-T-5%29%2B3%28T-5%29=61
2%2829-T%29%2B3T-15=61
58-2T%2B3T-15=61
43%2BT=61
T=61-43
T=18
go to
E=34-T.........eq.1,substitute T
E=34-18
E=16


Ellen is 16 and Todd is 18 years old now