# Mrs. Wang is 23 years older than her daughter, In 5 years, their ages will total 63, How old are they now?

Nov 10, 2016

Mrs. Wang is 38 years old and her daughter is 15 years old.

#### Explanation:

Let $\textcolor{red}{x} =$ the daughter's age

Mrs. Wang is $23$ years older, so her age is $\textcolor{b l u e}{x + 23}$

In five years, the daughter will be $\textcolor{red}{x + 5}$ years old

In five years, Mrs. Wang will be $\textcolor{b l u e}{x + 23 + 5} = \textcolor{b l u e}{x + 28}$ years old

And, in five years the sum of their ages will be 63, so...

$\textcolor{red}{x + 5} + \textcolor{b l u e}{x + 28} = 63$

Combine like terms

$2 x + 33 = 63$
$\textcolor{w h i t e}{a a} - 33 \textcolor{w h i t e}{a} - 33 \textcolor{w h i t e}{a a a}$Subtract 33 from both sides

$2 x \textcolor{w h i t e}{a a a a a} = 30$

$\frac{2 x}{2} = \frac{30}{2} \textcolor{w h i t e}{a a a}$Divide both sides by 2

$\textcolor{red}{x = 15} \textcolor{w h i t e}{a a a}$The daughter is 15

$\textcolor{b l u e}{x + 23} = 15 + 23 = \textcolor{b l u e}{38} \textcolor{w h i t e}{a a a}$Mrs. Wang is 38