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The sum of the ages of Frank and John is 54 years. 2 years ago, Frank was 4 times as...

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lucky092569 | Honors

Posted January 29, 2009 at 3:21 AM via web

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The sum of the ages of Frank and John is 54 years. 2 years ago, Frank was 4 times as old as John. Find John's age.

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enotechris | College Teacher | (Level 2) Senior Educator

Posted January 29, 2009 at 6:10 AM (Answer #1)

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Right now, Frank + John = 54.

1)  F + J = 54

But 2 years ago, Both Frank and John were 2 years younger each, which meant the sum of their ages is different by 4 years

2)  F + J = 54 - 4 = 50

And 2 years ago, Frank was 4 times older than John

3)  F = 4J

If we substitute eq. 3 for F in eq 2, we have

4)  4J + J = 50

5)  5J = 50

6)  J = 10

But John was 10 2 years ago, so now his age is 12. Substituting his current age in eq. 1

7)  F + 12 = 54

8)  F = 42, so currently Frank is 42 and John is 12. Two years ago, Frank was 40 and John 10.

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revolution | College Teacher | Valedictorian

Posted July 31, 2010 at 10:11 PM (Answer #2)

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Right now, F+J = 54 years

But two years ago, both of them were two years younger than now, so the sum of their age would be different by four years, so:

F+J= 54-4=50 years - eqn 1

Also, Frank was four times as old as John so:

F= 4J - eqn 2

Sub eqn 2 to eqn 1

4J+J=50

5J=50

J=10 years

Since John was age of 10 two years earlier, so his present age would be 10+2= 12 years.

So, now the earlier eqn would look like that

F+12=54

F+12-12=54-12

F=42. Thus, frank is 42 years of age while John is 12 years of age.

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