Question

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

Answer 1

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

Explanation:

Let `color(red)x=` the daughter's age

Mrs. Wang is `23` years older, so her age is `color(blue)(x+23)`

In five years, the daughter will be `color(red)(x+5)` years old

In five years, Mrs. Wang will be `color(blue)(x+23 + 5 )=color(blue)(x+28)` years old

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

`color(red)(x+5)+color(blue)(x+28)=63`

Combine like terms

`2x+33=63`
`color(white)(aa)-33color(white)(a)-33color(white)(aaa)`Subtract 33 from both sides

`2xcolor(white)(aaaaa)=30`

`(2x)/2=30/2color(white)(aaa)`Divide both sides by 2

`color(red)(x=15)color(white)(aaa)`The daughter is 15

`color(blue)(x+23)=15+23=color(blue)(38)color(white)(aaa)`Mrs. Wang is 38