# Mavis is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old is each now?

Sep 1, 2016

Mavis is now 15 years old and his brother 10 years old.

#### Explanation:

let Mavis's brother age now is A ,
So Marvis age is A+5
5 years ago, Marvis brother's age was A-5, Marvis's age was 2 times his brother's, so Marvis' age was 2(A-5)
Five years ago, Marvis' age was 2(A-5), now 5 years have passed, his age is 2(A-5) +5 = A+5.
$2 \left(A - 5\right) + 5 = A + 5$
$2 A - 10 + 5 = A + 5$
$2 A - 5 = A + 5$
$A = 10$
$A + 5 = 15$

Sep 1, 2016

The brother is 10 years old, Mavis is 15 years old.

#### Explanation:

We are working with 2 people and 2 periods of time;

Mavis and her brother, and their ages now and 5 years ago.

Her brother is younger - let his age be $\textcolor{b l u e}{x}$ years

Mavis is 5 years older than her brother (ADD 5)

For both of them, their ages were $\textcolor{\lim e}{\text{5 years LESS}}$, 5 years ago.

Write an expression for each person for each time.

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

$\text{Mavis} : \textcolor{w h i t e}{\times} \left(x + 5\right) - 5 = \textcolor{red}{x} \textcolor{w h i t e}{\times \times \times \times} \left(x + 5\right)$

$\text{Brother} : \textcolor{w h i t e}{\times} \textcolor{red}{\left(x - 5\right)} \textcolor{w h i t e}{\times \times \times \times \times \times x} \textcolor{b l u e}{x}$

The information we are given shows the relationship between their ages 5 years ago - shown in red.

At that time, she was TWICE as old as he was. Form an equation.
Do not multiply her age by 2!!

2 x younger age = older age

$2 \left(x - 5\right) = x$
$2 x - 10 = x$
$\textcolor{b l u e}{x = 10} \leftarrow$ this is the brother's present age.

The brother is 10 years old, Mavis is 15 years old.

Let's check:
$\textcolor{w h i t e}{\times \times \times x} 5 \text{ years ago" color(white)(x) larr color(lime)((-5)) larr color(white)(x) "present}$

$\text{Mavis} : \textcolor{w h i t e}{\times \times \times x} 10 \textcolor{w h i t e}{\times \times \times \times \times \times x} 15$

$\text{Brother} : \textcolor{w h i t e}{\times \times \times} \textcolor{red}{5} \textcolor{w h i t e}{\times \times \times \times \times \times x} \textcolor{b l u e}{10}$

$2 \times 5 = 10$