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# math problem

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Four years ago Arthur is 11 times as old as his son Arthur Jr, but four years from now, Arthur will only be \(4\) times as old as Jr. What is Arthur’s age when he is twice as old as Arthur Jr?

Mar 7, 2022

#1
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a = arthur now

(a-4) = 11 (j-4)      and     (a+4) = 4 (j+ 4)

a = 11j -40                         11j-40 + 4 = 4j+ 16        shows j = 8          then a = 48

now find when he is twice as old as j

a + x   = 2 ( j+x)

48 + x = 2(8) + 2x

32 = x                                     32 years from now    arthur = 80   j = 40 y/o

Mar 7, 2022
#2
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EP: Your 2 equations: (a-4) = 11 (j-4),   (a+4) = 4 (j+ 4), solve for a, j  give the following fractional results:

a = 292/7 and j = 52/7  [I think there is a mistake in the question] !!

Mar 7, 2022
#3
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Yep, I believe you are correct..... there is a problem with the Q   AND my solution had a math error !   D'Oh ! ~ EP

Let's use the correct numbers (thanx , Guest !)

a = arthur now

(a-4) = 11 (j-4)      and     (a+4) = 4 (j+ 4)

a = 11j -40                         11j-40 + 4 = 4j+ 16        shows j = 52/7      then a = 292/7

check:    4 years ago   j = 24/7      a = 264/7         CHECK !

check     4 years from now   j = 80/7      a = 320/70     CHECK !

Now find when a is twice as old

11j-40 + x    =   2 ( j+x)

11(52/7) - 40   + x   = 104/7 + 2x

188/7 = x                  188/7 years from now   a   will be twice as old as   j        CHECK !

ElectricPavlov  Mar 7, 2022
edited by Guest  Mar 7, 2022