Let 'x' be the number of calories per cup of popcorn, and 'y' be the number of calories per ounce of soda.
Given that 3 cups of popcorn and 6 oz of soda constitute 246 calories,
[tex]3x+6y=246[/tex]Also given that 1 cups of popcorn and 14 oz of soda constitute 274 calories,
[tex]x+14y=274[/tex]Solve the equations using Elimination Method.
Subtract 3 times equation 2 from equation 1,
[tex]\begin{gathered} (3x+6y)-3(x+14y)=246-3(274) \\ 3x+6y-3x-42y=246-822 \\ -36y=-576 \\ y=16 \end{gathered}[/tex]Substitute this value in equation 1, to obtain 'x' as,
[tex]\begin{gathered} 3x+6(16)=246 \\ 3x+96=246 \\ 3x=150 \\ x=50 \end{gathered}[/tex]Thus, the solution of the system of equations is x=50 and y=16.
Therefore, there are 50 calories per cup of popcorn, and 16 calorie per ounce of soda.
