To start out, we'll take into account that there are four variables, two of which we know the value for in Part A:
The total price Jamie paid. We know this is $85.
The buy-in, or the amount Jamie had to pay in order to purchase any squares. We'll use 'a' for this.
The number of squares Jamie bought. We know this is 15.
The cost per square. We'll use 'b' for this.
We can now model our situation as requested in Part A.
Since the total price is the sum of the buy-in and the total cost of the squares (which is the number of squares multiplied by the cost per square), our equation looks like this:
price = buy in + squares * cost per square
We can substitute in the values as defined above:
85 = a + 15 * b
There's our solution for Part A.
Now that we have that equation, and Part B has handed us $5 for the cost per square, we can substitute that in for b.
85 = a + 15 * 5
Now we can solve for a, or the buy-in price that Part B is asking us for.
Multiply the 15 and the 5:
85 = a + 75
Subtract 75 from both sides:
10 = a
There we have it. Our answer for Part B is that the buy-in to the pool was $10.
