Community gym charges a $50 membership fee and a $55 monthly fee. workout gym charges a $200 membership fee and a $45 monthly fee. after how many months will the total amount of money paid to both gyms be the same? what will, the amount be? what will the amount be

$50 + $55x 
x is the months that the member attends 
$200 + $45x 
We are looking for when the amount of money will be the same, so we'll set both equations equal to each other to find for x.
$50 + $55x = $200 + $45x 
        -$45x                -$45x
Isolate the variable
$50 + $10x= $200 
-$50              -$50
Subtract to get x to one side
$10x= $150
÷10      ÷10
Divide by ten
x= 15 
So it will take 15 months for both gyms to have the same amount of money paid.