age question for math

Question

in 5 years i will be 3 years older than my son. Together our age will be 68. how old are we now?

can you solve it

Answer 1

Sure I can solve it. I've seen dozens of versions of this one over the years. The key is to stay very organized -- I mean more than usual! We have two people with two different ages, so we'll arrange them thus:

 

                                    Age now                    Age in 5 years

 

Parent                                P                                  P + 5

 

Son                                   S                                  S + 5

 

We know two different facts that generate two different equations:

P + 5                    = 3 ( S + 5)

(P + 5) + (S + 5)   = 68

We need to simplify each equation, though, before working with them:

P + 5     = 3S + 15

P + S + 10  = 68

This builds a linear system, which means two options: the addition or substitution methods. Both work here, but it looks to my eyes that substitution is easier, so let's hop on that train:

P + 5  = 3S + 15

    -5              -5

 

P  = 3S + 10          Now we can replace the P in the other equation:

3S + 10 + S + 10 = 68

4S + 20  =  68        ...and solve for the "S":

       -20     -20

4S          = 48

4S / 4  = 48 / 4

S   = 12

Remember that we got P alone already? Just substitute back into that equation:

P = 3S + 10

P = 3 (12) + 10

  =  36 + 10

  = 46

Returning to that table up top, the parent is now 46 and will later be 51. Son is 12 and will reach 17. If you divide, you will find that 51 / 17 is indeed 3, so it fits the pattern.