# Hannah and Francine have $120. Hannah and Peter have $230. Peter has 6 times as much as much money as Francine. how much money does Hannah have?

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Let Hanna's money be represented by the variable: x.

Let Francine's money be represented by the algebraic expression: 120 - x

Peter's money can be represented by 6 times Francines or 6(120 - x)

Hannah an Peter have 230 therefore, Hannah's money + Peter's money = 230

`x + 6(120 - x) = 230` .

`x + 720 - 6x = 230`

`-5x = -490`

`x = 98`

**Since x represents the amount of money Hannah has, Hannah has $98.**

Once we have created our equation all we need to do is solve for X using inverse operations, here is a video explaining more steps:

Hannah and Francine have $120. Hannah and Peter have $230. Peter has 6 times as much as much money as Francine.

Let the amount with Hannah be represented by x.

As Hannah and Francine have $120, the amount with Francine is 120 - x

As Hannah and Peter have $230, the amount with Peter is 230 - x

Now Peter has 6 times as much as much money as Francine. This gives:

230 - x = 6*(120 - x)

230 - x = 720 - 6x

5x = 490

x = 490/5

x = 98

This gives the amount with Hannah as $98