Question

Mario kept all of his movie and popcorn receipts for an entire year. The movie tickets were $7.00 each and all together he spent $220.50. There were only three visits that he did not buy popcorn. He has a total of 45 receipts. How much did each bag of popcorn cost?

Answer 1

Let the number of movie receipts be x and number of popcorn receipts be y.

`x+y=45\ldots(i)`

It is also given that he spent 220.50 altogether.

Let the price of popcorn be z.

`7x+zy=220.50\ldots(ii)`

It is also given that on three occasions, he did not buy popcorn so it follows:

`x-y=3\ldots(iii)`

Add (i) and (iii) to get:

`\begin{gathered} 2x=48 \\ x=24 \end{gathered}`

So it follows:

`y=x-3=24-3=21`

Substitute the values x=24 and y=21 in (ii) to get:

`\begin{gathered} 7(24)+z(21)=200.50 \\ 21z=200.50-168 \\ 21z=32.5 \\ z=(32.5)/(21)=1.547619048\approx1.55 \end{gathered}`

So each bag of popcorn costed approximately 1.55 dollars.