Mr. Flanders' class sold doughnuts for $1.35 each and Mr. Rodriquez's class sold cartons of milk for $1.08 each together the classes sold 85 items and earned $104.49 for their school. How many of each item did the classes sell?

A define the variables in this situation

B write a system of equations that model the problem

C use the linear combination method to find the solution to the solution to the system you wrote in part b show all your work

D using a complete sentence explain what the solution found in part c represents

Part A: Let, the number of doughnuts = x and the number of carton milk = y.

Part B: We have, Mr. Flanders sold doughnut for $1.35 each and Mr. Rodriquez sold milk for $1.08 each.

As, they sold 85 items in total.

Thus, x + y = 85.

Moreover, they both earned $104.49 in total.

So, 1.35x + 1.08y = 104.49.

Hence, we get the system of equations,

1.35x + 1.08y = 104.49

x + y = 85.

Part C: Now, we will solve the system of equations,

As, x + y = 85 ⇒ y = 85 - x.

As, 1.35x + 1.08y = 104.49 ⇒ 1.35x + 1.08 (85-x) = 104.49 ⇒ 1.35x + 91.8 - 1.08x = 104.49 ⇒ 0.27x = 12.69 ⇒ x = 47.

So, y = 85 - 47 ⇒ y = 38.

Thus, x = 47 and y = 38 is the solution.

Part D: Hence, we get that,

Number of doughnuts sold by Mr. Flanders is 47 and the number of carton milk sold by Mr. Rodriquez is 38.