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

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Answer 1 · 2016-11-10T04:44:21

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

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