SOLUTION: Dan’s mother is 55 years old. If three years ago. The difference of their ages is two less than dan’s dage was, how old is dan now?

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Question 1194619: Dan’s mother is 55 years old. If three years ago. The difference of their ages is two less than dan’s dage was, how old is dan now?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dan, d
Mother, 55
Mother three years ago, 52
Description: 52-%28d-3%29=-2%2B%28d-3%29

SOLVE
52=-2%2B2%28d-3%29
54=2%28d-3%29
27=d-3
highlight%28d=30%29

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


The solution from the other tutor starts by letting Dan's age be x, because that is what the problem asks you to find.

That is of course a valid way to set up the problem.... But it leads to unnecessarily awkward equations, which are difficult for a beginning student to form from the given information.

Here is a different start which leads to a much simpler solution.

Let x = Dan's age 3 years ago

Then x-2 = the difference in their ages (the difference in their ages is 2 less than Dan's age 3 years ago)

So x+(x-2)=2x-2 = Dan's mother's age 3 years ago

So then Dan's mother's age now is (2x-2)+3 = 2x+1

His mother is now 55: 2x+1=55; 2x=54; x=27. Dan's age 3 years ago was x=27.

So Dan's age now is 27+3 = 30.

ANSWER: Dan is 30