Question

Question #eae6b

Answer 1

Peter is 13 and Luke is 24.

Explanation:

Suppose Luke is `L` years old and Peter is `P` years old.

Here is how you write "Luke's age is 2 less than twice Peter's age":
`L = 2P-2`

Here is how your write "The sum of their ages is 37":
`L+P=37`

We can replace `L` with `2P-2` in the second equation.

`color(red)L" "+P=37`
`color(red)(2P-2)+P=37`
`3P-2=37`
`3P=39`
`P=13`. So Peter is 13 years old.

Now you can replace `P` with `13`

`L=2*color(red)P-2`
`L=2*color(red)13-2`
`L=26-2`
`L=24`. So Luke is 24 years old.