I use what I call “Let” statements to help define the variables and quantities in word problems. Once that’s done, the equation pretty much falls into place.

Let M = the number of members prior to the new ones joining

Let N = the number of members after the new ones joined

Let A = the new assessment per member

Let B = the old assessment per member

Now let’s see what they’ve given us to work with.

We know that M * B = 1200. We know that A = B – 7.50. We also know that the amount of money the club desires to raise stays the same… so…

A * (M + 8) = 1200

There are other ways to put the equations together, but this is the method you’d use to solve these kinds of word problems. I hope this helps you.