Question

The sum of Lisa's age and Patrick's age is 38 while the difference of their ages is 8. if Patrick is older than Lisa, how old is Patrick?

Answer 1

$\text{Patrick is 23 years old}$

We start by assigning variables to represent their ages

Let Lisa's age be represented by l and Patrick's age be represented by p

First part of the question states that the sum of their ages is 38

Mathematically;

$l\text{ + p = 38 }\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i_{})$

The difference of their ages is 8, and since Patrick is older, we have the equation as;

$\begin{gathered} p\text{ - l = 8} \\ \\ \text{This means} \\ \\ p-8\text{ = l }\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots..(ii) \end{gathered}$

Now substitute equation ii into i; we have

$\begin{gathered} p\text{ - 8 + p = 38} \\ \\ 2p\text{ - 8 = 38} \\ \\ 2p\text{ = 38 + 8} \\ \\ 2p\text{ = 46} \\ \\ p\text{ = }\frac{46}{2} \\ \\ p\text{ = 23} \end{gathered}$