Question

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

Answer 1

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(A-5)+5 = A+5`
`2A-10+5=A+5`
`2A-5=A+5`
`A=10`
`A+5=15`

Answer 2

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 `color(blue)( x)` years

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

For both of them, their ages were `color(lime)("5 years LESS")`, 5 years ago.

Write an expression for each person for each time.

`color(white)(xxxxxxx) 5 " years ago" color(white)(x) larr color(lime)((-5)) larr color(white)(x) "present"`

`"Mavis":color(white)(xx)(x+5)-5 = color(red)(x) color(white)(xxxxxxxx)(x+5)`

`"Brother":color(white)(xx)color(red)((x-5)) color(white)(xxxxxxxxxxxxx)color(blue)(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(x-5) = x`
`2x-10=x`
`color(blue)( x= 10) larr` this is the brother's present age.

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

Let's check:
`color(white)(xxxxxxx) 5 " years ago" color(white)(x) larr color(lime)((-5)) larr color(white)(x) "present"`

`"Mavis":color(white)(xxxxxxx)10 color(white)(xxxxxxxxxxxxx)15`

`"Brother":color(white)(xxxxxx)color(red)(5) color(white)(xxxxxxxxxxxxx)color(blue)(10)`

`2 xx5 = 10`