24.6k views
5 votes
At a local pizza place, the cost for 3 small pizzas and 3 medium pizzas is $51. The cost for 5 small and 2 medium is $55. How much will it cost for 3 small and 2 medium pizzas? A) $35 B) $53 C) $41 D) $50

User RyPope
by
8.6k points

1 Answer

3 votes

Let x be the cost for the small pizza and y the cost for the medium one. We know that 3 small ones and 3 medium ones cost $51, this can be express as:


3x+3y=51

we also know that 5 small ones and 2 medium ones cost $55, this means that:


5x+2y=55

Then we have the system of equations:


\begin{gathered} 3x+3y=51 \\ 5x+2y=55 \end{gathered}

Multipliyng the first equation by 2 and the second by -3 we have:


\begin{gathered} 6x+6y=102 \\ -15x-6y=-165 \end{gathered}

Adding the equations we have:


\begin{gathered} -9x=-63 \\ x=(-63)/(-9) \\ x=7 \end{gathered}

Once we know the value of x we plug it in the first equation and solve for y, then:


\begin{gathered} 3(7)+3y=51 \\ 21+3y=51 \\ 3y=30 \\ y=10 \end{gathered}

Hence, a small pizza cost $7 and a medium one cost $10.

now that we have the cost of each of them we can obtained the cost for 3 small and 2 medium:


3(7)+2(10)=41

Therefore, 3 small and 2 medium pizzas cost $41. The answer is C.

User Shlok Nangia
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories