Question

Betty is 3 times as old as Mike. In 5 years, she will be twice as old. How old are they now?

Answer 1

Betty is 15.

Mike is 5.

Explanation:

We can let Betty's age be b and Mike's age be m.

Since Betty's age is 3 times of Mike, then

`b=3m`

In 5 years, the age of Betty and Mike would be
`b+5` and
`m+5` respectively.

Since Betty is 2 times as old as Mike then, then
`b+5=2(m+5)`.

We know that
`b=3m`, so we can substitute that:

`3m+5=2(m+5)`

Expand:

`3m+5=2m+10`

Subtract 5 from both sides:

`3m+5-5=2m+10-5`

`3m=2m+5`

Subtract 2m from both sides:

`3m-2m=2m+5-2m`

`m=5`.

Mike is 5 years old.

Since Betty is 3 times as old as Mike, Betty's age is
`5*3=15`