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Five years ago, Amy was 20 years younger than her father, this year she IS half her fathers age. How old is Amy?
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A - 5 = (F-5) - 20, (1) ("Five years ago, Amy was 20 years younger than her father")
2A = F. (2) ("this year she is half her fathers age")
Substitute (2) into (1), i.e. replace F in the right side of (1) by 2A, according (2). You will get
A - 5 = 2A - 5 - 20, or
20 = A.
Answer. Amy is 20 years old now. Her father is 2*A = 2*20 = 40 years.
The phrase "Five years ago, Amy was 20 years younger than her father" seems to be strange.
If five years ago Amy was 20 years younger than her father, then she will be always 20 years younger until both are alive.
The phrase "this year she will be half her fathers age" is BAD and is never used in this kind of problems.
Because it creates unnecessary thoughts in the reader's mind.
Its only destination is to confuse the reader.
There is a bunch of lessons on age word problems
- Age problems and their solutions
- A fresh formulation of a traditional age problem
- Really intricate age word problem
- Selected age word problems from the archive
- OVERVIEW of lessons on age problems
in this site.
Read them and become an expert in solving age problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
It contains a lot of other word problems and many other interesting and useful things.