Question

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

Answer 1

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.