Easy Age Problem: 2

Algebra Level 3

Peter is 36 years old. Peter is twice as old as Jun was when Peter was as old as Jun is now. How old is Jun?

Note: Be mindful of their past and present age


The answer is 24.

Rhiana Vanessa Bag-id Amoin by Rhiana Vanessa Bag-id Am… , 25

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2 solutions

Joram Otero
Jul 3, 2014

Peter's age = 36
Jun's age = J
Difference between their age X = 36 - J

Peter is twice as old as Jun was when Peter was as old as Jun is now.

36 - X = (J - X) (2)

36 - X = 2J - 2X

36 - (36 -J) = 2J - 2(36-J)

3J = 72

J = 24

please reply to this solution if you have some clarifications. thank you.

0 Helpful 1 Interesting 1 Brilliant 0 Confused

It says 'Peter is twice as old as Jun was', so shouldn't the first line of the calculation be: 36 = (J - X) (2)

So: 36 = 2J - 2X 36 = 2J - 2(36 - J) 36 = 4J - 72 108 = 4J J = 27

Matthew Jensen - 6 years, 11 months ago

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Sorry for bad formatting, here is calculation again:

36 = 2J - 2X

36 = 2J - 2(36 - J)

36 = 4J - 72

108 = 4J

J = 27

Matthew Jensen - 6 years, 11 months ago

Peter "was"...(meaning x), Peter "is"...(meaning 36), Jun "was"... (meaning x/2), Jun "is"... (meaning x)

The time elapsed for Peter and for Jun are equal. So, 36-x = x-x/2 solve for x. We obtain, 24.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I cannot follow your reasoning for Jun "was" being x/2 as Peter IS twice as old as Jun was, so Jun "was" should be 36/2 which is 18. Taking P1 to be Peter was, P2 to be Peter now (36), J1 to be Jun was and J2 to be Jun now. J1=18. If x is the difference in ages between "was" and "now" then J1+x=J2. P1+x=36. But P1=J2 so J2+x=36. Solving simultaneously gives x=9. So P1=27 which means J2 is also 27.

Filly Mare - 6 years, 11 months ago

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please take a look at my solution. thanks!

joram otero - 6 years, 11 months ago

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