Question

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

Answer 1

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`

Answer 2

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!.