SOLUTION: Mary's age is 4 years younger than half her mothers age. If the total of their age is 56, how old are they?

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Question 1132337: Mary's age is 4 years younger than half her mothers age. If the total of their age
is 56, how old are they?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
m, Mother
m%2F2-4, Mary

Total Age Sum, 56
m%2B%28m%2F2-4%29=56
-
m%2Bm%2F2=60
3m%2F2=60
highlight%28m=40%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We could let x be the mother's age; then Mary's age would be (1/2)x-4. But working with fractions always slows down the computations; so

let 2x = mother's age
then x-4 = Mary's age

Write and solve the equation that says the sum of those two ages is 56.

I leave that to you.

For an informal solution using logical reasoning instead of formal algebra, try this:

(1) Add 4 years to Mary's age, making her half as old as her mother; the sum of their ages is now 60
(2) Determine the two ages if Mary is half as old as her mother and the sum of the two ages is 60
(3) Subtract the 4 years you added from Mary's age to get her real age

If you solve the problem by the formal algebraic method, you will see that it does exactly the same calculations as the informal method.