Question

Matthew is 3 times as old as jenny. in 7 years, he will be twice as old as she will be then. how old is each now? Explain how to solve it to plz

Answer 1

Let m and j be the current ages of Matthew and Jenny, respectively.

Now, Matthew is 3 times as old as Jenny, so the variables are in the following relation:

$m=3j$

In 7 years, both of them will be 7 years older, i.e. their ages will be m+7 and j+7, and Matthew will be twice as old:

$m+7=2(j+7)$

Now, remembering that m=3j, we can rewrite the second equation as

$3j+7=2j+14 \iff j = 7$

So, Jenny is 7 and Matthew is 21 (he's 3 times older).

In fact, in 7 years, they will be 14 and 28, and Matthew will be twice as old.