Pat is 23 years older than his son Patrick. In 5 years pat will be twice as old as Patrick. How old are they now

Question

Pat is_____ years old while Patrick is ____years old

Answer 1

Hi Fatima,

You asked how to solve the following: "Pat is 23 years older than his son Patrick. In 5 years Pat will be twice as old as Patrick. How old are they now?

One way to solve this is by approaching it as an algebraic system of equations.

I'm going to use S to represent the son, Patrick's, age. I'm going to use F to represent the father, Pat's, age.

Right now, if we add 23 years to the son's age, we get the father's age. I can write that as follows.

S + 23 = F

In 5 years, both the son and the father will be five years older. Their ages will be S+5 and F+5.

We also know that F+5 will be twice S+5. I can write an equation to represent that as follows:

F + 5 = (S + 5) x 2

Now I have two equations. I can substitute S + 23 for F because they are equal. If I do this, I create a one-variable equation that can be solved:

(S + 23) + 5 = (S + 5) x 2

If I simplify that, I get the following:

S + 28 = 2S + 10

Continue to solve for S, the son's age. Once you know the son's age, you can solve for the father's age.

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Answer 2

Patrick is currently 18 years old. Pat is currently 41 years old. (18 + 23 = 41)

In five years: Patrick will then be 23 years old (18 + 5 = 23)

Pat will then be 46 years old (41 + 5 = 46)

23 x 2 = 46 (making 46 twice as much as 23)