Elena is now four times as old as Lizette. Five years ago, the sum of their ages was 45. How old is each now?

2 Answers
Jun 14, 2017

Answer:

Elenea is #44# years old and Lizette #11#.

Explanation:

Call the present ages of Elena and Lizette #e and l#; you get:

#e=4l#

#(e-5)+(l-5)=45#

Substitute the first into the second and rearrange:

#4l-5+l-5=45#

#5l=55#

#l=11#

so that

#e=4*11=44#

Jun 14, 2017

Answer:

Lizette is #11# and Elena is #4xx11 = 44#

Explanation:

There are 2 people and 2 periods of time (past and present)

Choose a variable and write an expression for the age of each person for each period of time..

Lizette is younger, so let her age be #x# years.
Elena is four times as old, so her age is #4x# years

#5# years ago they were both #5# years younger.

#color(white)(xxxxxxx)ul("(5 years ago"color(white)(xxxxx)"present")#

Lizette#color(white)(xxxxx)color(blue)((x-5))color(white)(xxxxxxxx)x#
Elena#color(white)(xxxxx)color(blue)((4x-5))color(white)(xxxvvvxx)4x#

The sum of their ages #5# years ago was #45# years.

Write an equation to show this:

#color(blue)((x-5)+(4x-5) = 45)#

#5x -10 = 45#

#5x = 45+10#

#5x = 55#

#x=11#

So, Lizette is #11# and Elena is #4xx11 = 44#

Check: #5# years ago: Lizette was #6# and Elena was #39#

#6+39 = 45#

It all checks out!.