# Height problem

1. Jan 2, 2016

### Natasha1

1. The problem statement, all variables and given/known data

Emily's brother, Jack, is now 105cm tall, having grown by one sixth of his height a year ago. How tall was Jack one year ago?

2. Relevant equations

Now my teacher told me to do this:

x = 105 - (105/7)
x = 105 - 15
x = 90 cm

3. The attempt at a solution

So 90cm is the answer. But can someone explain to me very simply why we divided by 7 the 105 as the question says that Jack grew by one sixth and not by one seventh? Many thanks.

2. Jan 2, 2016

### SammyS

Staff Emeritus
Maybe looking at it a different first would help.

Let x be Jack's height one year ago.

Add x plus x/6 to get 105.

Solve for x:
$\displaystyle \ x+\frac{x}{6}=105 \$

3. Jan 2, 2016

Ahh,

So 7x = 105
x = 15

4. Jan 2, 2016

### SammyS

Staff Emeritus
Actually it's more like:
$\displaystyle \ 7\left(\frac{x}{6}\right)=105 \ ,$​
so that
$\displaystyle \ \frac{x}{6}=\frac{105}7 \ ,$​
etc.