frank is 4 times as old as lin. The difference in their ages is equal to lins age plus 8. How old is each

Question

This is hard can u please help me

Answer 1

Let's set up two equations that relate the two people's ages.

 

We'll call Frank's age "F" and Lin's age "L."

 

We know Frank is the older of the two.

 

The first sentence gives us the equation F = 4L.

 

The second sentence talks about a difference -- but do we want to work with F - L or L - F? Since the difference is equal to Lin's age plus 8, which is positive, we need a positive difference. Frank is older, so the positive difference is F - L. (L - F would be negative).

 

So. the second sentence can be expressed as F - L = L + 8

 

So we have two equations with two variables:

 

F = 4L

F - L = L + 8

 

There are several ways to solve this type of problem but since the first equation is so simple, just replace all instances of F in the second equation with 4L!

 

You end up with the following:

 

4L - L = L + 8

 

At this point, it should be easy to solve for L, and find Lin's age. Frank's age is easy to find out after that by using the first sentence.