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

Jun 14, 2017

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

#### Explanation:

Call the present ages of Elena and Lizette $e \mathmr{and} l$; you get:

$e = 4 l$

$\left(e - 5\right) + \left(l - 5\right) = 45$

Substitute the first into the second and rearrange:

$4 l - 5 + l - 5 = 45$

$5 l = 55$

$l = 11$

so that

$e = 4 \cdot 11 = 44$

Jun 14, 2017

Lizette is $11$ and Elena is $4 \times 11 = 44$

#### 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 $4 x$ years

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

$\textcolor{w h i t e}{\times \times \times x} \underline{\text{(5 years ago"color(white)(xxxxx)"present}}$

Lizette$\textcolor{w h i t e}{\times \times x} \textcolor{b l u e}{\left(x - 5\right)} \textcolor{w h i t e}{\times \times \times \times} x$
Elena$\textcolor{w h i t e}{\times \times x} \textcolor{b l u e}{\left(4 x - 5\right)} \textcolor{w h i t e}{\times x \bigvee \times} 4 x$

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

Write an equation to show this:

$\textcolor{b l u e}{\left(x - 5\right) + \left(4 x - 5\right) = 45}$

$5 x - 10 = 45$

$5 x = 45 + 10$

$5 x = 55$

$x = 11$

So, Lizette is $11$ and Elena is $4 \times 11 = 44$

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

$6 + 39 = 45$

It all checks out!.