Question

two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90.write and solve a system of equations to determine the the price of one plain pizza(only an algebraic solution can receive full credit.)

Answer 1

Let:

x = Cost of one plain pizza

y = Cost of one soda

two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. so:

`\begin{gathered} x+2y=15.95_{\text{ }} \\ \end{gathered}`

later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90. so:

`3x+5y=45.90`

Let:

`\begin{gathered} x+2y=15.95_{\text{ }}(1) \\ 3x+5y=45.90_{\text{ }}(2) \end{gathered}`

From (1) solve for x:

`x=15.95-2y_{\text{ }}(3)`

Replace (3) into (2):

`\begin{gathered} 3(15.95-2y)+5y=45.90 \\ 47.85-6y+5y=45.90 \\ -y=-1.95 \\ y=1.95 \end{gathered}`

Replace the value of y into (3):

`\begin{gathered} x=15.95-2(1.95) \\ x=12.05 \end{gathered}`

Therefore, the price of one plain pizza is $12.05