SOLUTION: A woman is 4 times older than her child. 5 years ago the woman was 5 times the age of the child. Find the mothers age

Question 1140360: A woman is 4 times older than her child. 5 years ago the woman was 5 times the age of the child. Find the mothers age
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A woman is 4 times older than her child.
w = 4c
5 years ago the woman was 5 times the age of the child.
w - 5 = 5(c-5)
w - 5 = 5c - 25
w = 5c - 25 + 5
w = 5c - 20
replace w with 4c, from the 1st equation
4c = 5c - 20
20 = 5c - 4c
c = 20 yrs is the child's age
:
Find the mothers age
w = 4(20)
w = 80 yrs is the mother's age
:
:
Check in the statement
"5 years ago the woman was 5 times the age of the child."
80 - 5 = 5(20 - 5)
75 = 5(15)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Although another tutor solved the problem, it is in fact unsolvable as posed.

The trouble is that in everyday English the phrases "4 times older than" and "4 times as old as" are usually interpreted as meaning the same thing. However, that is grammatically incorrect.

In this problem, if the child's age is 8, then "4 times older than" the child means 8, plus 4 times 8, or 8+32 = 40. So grammatically "4 times older than" means the same as "5 times as old as".

With the correct interpretation of "4 times older than", this problem then says that a woman is 5 times as old as her child both now and 5 years ago. That is not possible.

So in fact the problem as posed has no solution.
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