John is now 3 times as old as his brother Sam. In 5 years, John will be twice as old as Sam will be then. Find their present ages.

Question

I don't understand the second part where it says, "In 5 years, John will be twice as old as Sam will be then."

Answer 1

J = John's present age

S = Sam's present age

 

Here is how I interpret the given information...

 

Present:

 

J = 3S (given)

 

In 5 years:

 

J → J + 5

S → S + 5

J + 5 = 2(S + 5) (given)

 

What we need to do is solve the following 2 equations in 2 unknowns J and S:

 

(i)   J = 3S

(ii)  J + 5 = 2(S + 5)

 

Substitute (i) into (ii) and get

 

3S + 5 = 2(S + 5)

 

S = 10 - 5 = 5

 

Substitute S = 5 in (i) and get

 

J = 3(5) = 15

 

Answer:  John is now 15, Sam is 5.