1
$\begingroup$

Bob and Alice have together a sum of $103$ years old. In $4$ years, Alice will have $2$ times the age of Bob.

What age will they have ?

I'm trying different equation and doing my substitution but I can't get a valid answer (a integer).

$ x+y = 103 ,$

$ (x+4) + (y+4) = 2x $

etc..

Thanks for help, it's appreciated !

  • 0
    In any solution, if you introduce variables, you should say what they stand for. That will help both you and the reader. It looks as if $x$ is Bob's current age, and $y$ is Alices's (not a great choice, potentially confusing to the reader and you). But let's go on. In terms of $x$, how old will Bob be in $4$ years? In terms of $y$, how old will Alice be in $4$ years? Alice will be twice Bob's age. What equation does that give us?2011-09-19

2 Answers 2

8

Consider an analogous problem: Art and Bill's answers currently have $31$ total upvotes. If both receive $4$ more upvotes then Art will have twice as many upvotes as Bill. How many is that?

Let $\rm\:A,B\:$ be the upvotes Art, Bill have after the $4$ upvotes. We are given $\rm\:A = 2\:B\:,\:$ and before the $4$ upvotes they had sum $31\:,\:$ i.e. $\rm\: A\!-\!4\:+\:B\!-\!4\: =\: 31\:.\:$ Hence $\rm\ 39 = A + B = 2\:B + B = 3\:B\:.\:$ Therefore $\rm\:B = 13\:$ and $\rm\:A = 2\:B = 26\:.\:$

Extra credit: Whose answer will be accepted?

  • 2
    +1 for the extra credit problem, which from empirical evidence seems to be independent of all known axioms.2011-09-19
1

Let $A$ and $B$ represent the original age of alice and bob.

You have to solve the following system of equations.

$A + B = 103$

$2(B + 4) = A + 4$


Thus $A = 103 - B$

So

$2B + 8 = 107 - B$

Therefore

$3B = 99$

$B = 33$ and $A = 70$.