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