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# John is 3/4 the age of James. Three years ago, John was 5/7 the age of James. How old is James?

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John is 3/4 the age of James. Three years ago, John was 5/7 the age of James. How old is James?

Jul 14, 2018

#1
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24

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Jul 14, 2018
#3
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Daniel, writing the answer 24 does not teach anyone anything.

We are here to teach people :)

Melody  Jul 14, 2018
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John is 3/4 the age of James. Three years ago, John was 5/7 the age of James. How old is James?

First thing I am going to do is change the names cause they are too confusing.

James becomes his twin sister Amy.

John is 3/4 the age of Amy. Three years ago, John was 5/7 the age of Amy. How old is Amy?

Let John's age now be J.  Three years ago his age was J-3

Let Amy's age now be A.        Three years ago her age was A-3

John is 3/4 the age of Amy.

so

$$J=\frac{3}{4}*A\\ J=\frac{3A}{4}$$

Three years ago, John was 5/7 the age of Amy.

$$J-3=\frac{5}{7}*(A-3)\\ J-3=\frac{5A-15}{7}\\ J=\frac{5A-15}{7}+3\\$$

so

$$\frac{3A}{4}=\frac{5A-15}{7}+3\\ 28*\frac{3A}{4}=28*[\frac{5A-15}{7}+3]\\ 21A=4(5A-15)+84\\ 21A=20A-60+84\\ A=24\\$$

Amy and therefore James, is 24 years old.

Jul 14, 2018
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This question was posted before here:

https://web2.0calc.com/questions/john-is-the-age-of-james-three-years-ago-john-was

Jul 14, 2018
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So what!

It was not answered and I specifically asked our guest to make a new post as the first one had omissions in it!