The pool membership has an initial fee of $350, afterwards you have to pay $125 per month.
Let "x" represent the number of months of the membership and "y" represent the total cost after x months, you can express the relationship between the number of months of the membership and the total cost as:
[tex]y=350+125x[/tex]The family paid $1350 for the membership, to determine the number of months they paid "x", you have to replace the equation with y=1350 as follows:
[tex]1350=350+125x[/tex]To calculate the value of x, first, pass 350 to the other side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 1350-350=350-350+125x \\ 1000=125x \end{gathered}[/tex]Next, divide both sides by 125 to reach the value of x:
[tex]\begin{gathered} \frac{1000}{125}=\frac{125x}{125} \\ 8=x \end{gathered}[/tex]The family used the pool for 8 months.