Mary McDonald makes mugs in Miami. She makes two sizes of mugs: a small mug that she sells for $2.50 and a large mug that she sells for $5.75. Yesterday Mary made $56. Before she opened her shop in the morning, she had 200 mugs in her inventory. At the end of the day she has 188. How many mugs of each price did she sell?

So for this one we need to find a system of equations in order to solve for each mug. We know that there were 12 total mugs sold because 200 - 188 = 12. So we can say m + M = 12 where m is small mugs and M is big mugs. We also know Mary made $56, and we know the prices of each mug. So we say 2.50m + 5.75M = 56. Now use the first equation to solve for m. Subtract M from both sides to get m = 12 - M. Now plug that into the second equation. So 2.50(12 - M) + 5.75M = 56. Thus 30 -2.50M + 5.75M = 56 and 3.25M = 26. Thus M = 8. Now plug that back into the other equation to get m + 8 = 12. Thus m = 4. So M = 8 and m = 4. Hope this helps. Let me know if you have any other questions.