# Lisa is 10cm taller than Ian. Ian is taller than than Jim by 14cm. Every month, all three grow 2cm each. In 7 months time, Ian's and Jim's combined heights will be 170cm greater than Lisa's. How tall is Ian?

$I = 180$

and just for fun:

$L = 190 , J = 166$

#### Explanation:

Ok... word problems! The way to solve these things is to write down into math symbology what is written on the page. So let's do that.

First off we have Lisa and Ian. So I'm going to let $L$ be Lisa's height and $I$ will be Ian's height. And everything will be in centimetres - so we can drop the units for now in the equations to make things cleaner.

Ok - Lisa is 10 taller than Ian. So we can write that as:

$L = I + 10$ (This says that Ian would have to be 10 taller to be the same height as Lisa)

Next sentence - and we have a new person, Jim (we'll let $J$ be Jim's height). Ian is taller than Jim by 14. So we write that:

$I = J + 14$

With me so far? Good!

Every month, $L , I , \mathmr{and} J$ increase by 2. This is good to know because of the next statement - in 7 month's time, Ian's height plus Jim's height will be 170 more than Lisa's.

Ok - so the amount that each of them grows in 7 months will be 14, because if it's 2 per month and it's 7 months, $7 \times 2 = 14$. We can now write that last bit in math terms as:

$J + 14 + I + 14 = L + 14 + 170$

And the question wants to know what Ian's height is.

To solve this, let's put the first two equations in terms of $I$ and then substitute it into this 3rd one:

$L = I + 10$ - this one is already in terms of $I$

$I = J + 14$ - let's adjust this one...

$J = I - 14$

Ok - we're all set.

$J + 14 + I + 14 = L + 14 + 170$

$\left(I - 14\right) + 14 + I + 14 = \left(I + 10\right) + 14 + 170$

$2 I + 14 = I + 194$

$I = 180$

and just for fun:

$L = 190 , J = 166$