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