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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

Answer 1

Answer: A. 'x' be the number of doughnuts sold and 'y' be the number of cartoons of milk sold.

B.
`x+y=85`

`1.35x+1.08y=104.49`

C. x=47 and y=38

D. The number of doughnuts sold x= 47 and the number of cartoons of milk sold= 38.

Explanation:

A. Since there are only two quantities i.e. doughnuts and cartons of milk.

So let 'x' be the number of doughnuts sold and 'y' be the number of cartoons of milk sold.

B. The total number of items sold =
`x+y=85`

The total amount they earned=
`1.35x+1.08y=104.49`

∴ The system of equations that model the problem will be

`x+y=85`.........(1)

`1.35x+1.08y=104.49`.............(2)

C. To apply linear combination method multiply eqn(1) by 1.5 we get

`1.35x+1.35y=114.75`....(3)

Now subtract eq(2) from eqn(3), we get

`0.27y=10.26\\\Rightarrow\ y=(10.26)/(0.27)\\\Rightarrow\ y=38`

From (1), we get x=85-38=47

D. From C part the number of doughnuts sold x= 47 and the number of cartoons of milk sold= 38.