We have 2 equations with 2 unknowns.
Marcos buys 6 pepperoni (P) and 2 cheese pizzas (C) and spends $98, so we can write:
[tex]6P+2C=98[/tex]P: price of pepperoni pizza
C: price of cheese pizza
Chucky buys 2 pepperoni and 6 cheese pizzas and spends $86. Then we can write:
[tex]2P+6C=86[/tex]To find P, the price of the pepperoni pizza, we can substitute the first equation in the second equation as:
First equation:
[tex]\begin{gathered} 6P+2C=98 \\ 2C=98-6P \\ C=\frac{98-6P}{2} \\ C=49-3P \end{gathered}[/tex]Second equation:
[tex]\begin{gathered} 2P+6C=86 \\ 2P+6(49-3P)=86 \\ 2P+6\cdot49-6\cdot3P=86 \\ 2P+294-18P=86 \\ -16P=86-294 \\ -16P=-208 \\ P=\frac{-208}{-16} \\ P=13 \end{gathered}[/tex]The price of the pepperoni pizza is $13.
