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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?

User Manan Shah
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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.

User Smolla
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