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.

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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: