When setting up your formulas to work this, you need to see how many variables are unknown. You have two: the number of $10 sets and the number of $45 sets.
Like TchrWill shows, you can set a variable for each of these numbers you don't know:
x = number of $10 sets
y = number of $45 sets
Again, like TchrWill shows, you can set (x + y) equal to 200, because you're given the information that the manager only wants to buy 200 sets total. So, your first equation is:
x + y = 200
Then you know that the cost of the total number of $10 sets is the number of sets bought times the price of each set:
10*x
Likewise, the cost of the total number of $45 sets is the number of sets bought times the price of each set:
45*y
Also, you know that the total amount the manager is willing to pay for all these plates is $7250. So you can set the costs of each of the plate sets equal to that amount:
10*x + 45*y = 7250
So now your two equations are:
x + y = 200
and
10*x + 45*y = 7250
Rearrange the first equation to solve for y:
y = 200 - x
plug this in for y in the second equation and solve for x:
10*x + 45*(200-x) = 7250
10*x + 9000 - 45*x = 7250
10*x - 45*x = -1750
-35*x = -1750
x = 50
Plug x into your first equation (x + y = 200) to solve for y:
50 + y = 200
y = 150
Now plug x and y into all your equations to make sure your value work!
http://tinyurl.com/28esbw
If it worked, that means that the manager had to buy 50 (your x-value) of the $10 sets and 150 (your y-value) of the $45 sets.
