Let the number of movie receipts be x and number of popcorn receipts be y.
[tex]x+y=45\ldots(i)[/tex]It is also given that he spent 220.50 altogether.
Let the price of popcorn be z.
[tex]7x+zy=220.50\ldots(ii)[/tex]It is also given that on three occasions, he did not buy popcorn so it follows:
[tex]x-y=3\ldots(iii)[/tex]Add (i) and (iii) to get:
[tex]\begin{gathered} 2x=48 \\ x=24 \end{gathered}[/tex]So it follows:
[tex]y=x-3=24-3=21[/tex]Substitute the values x=24 and y=21 in (ii) to get:
[tex]\begin{gathered} 7(24)+z(21)=200.50 \\ 21z=200.50-168 \\ 21z=32.5 \\ z=\frac{32.5}{21}=1.547619048\approx1.55 \end{gathered}[/tex]So each bag of popcorn costed approximately 1.55 dollars.
