SOLUTION: The sum of James’ age and David’s age is 34. Five years ago, the sum of twice James’ age and three times David’s age was 61. What are their present ages
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Question 1109968: The sum of James’ age and David’s age is 34. Five years ago, the sum of twice James’ age and three times David’s age was 61. What are their present ages Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39616) (Show Source):
The condition gives you two equations
J + D = 34, (1)
2*(J-5) + 3*(D-5) = 61. (2)
Simplify (2):
2J - 10 + 3D - 15 = 61,
2J + 3D = 61 + 10 + 15,
2J + 3D = 86. (3)
From (1), J = 34-D. Substitute it into (3). You will get the single equation for only one unknown D:
2*(34-D) + 3D = 86, (It is how the Substitution method works).
68 - 2D + 3D = 86 ====> D = 86 - 68 = 18.
Answer. David is 18 years old. James is 34-18 = 16 years old.
Check. 2*(16-5) + 3*(18-5) = 2*11 + 3*13 = 22 + 39 = 61.
Solved. // On the way, you learned on how the Substitution method works.
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