Question #eae6b

1 Answer
Feb 3, 2017

Answer:

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.