Question

Ms. Doyle is having a party for her dass. She pay $5 for pizza and $2 for a drink. If she bought 20 total items for $46, how many pizzas did she buy?

Answer 1

Step-by-step explanation:

• x: number of pizzas

,

• y: number of drinks

We can write a system of equations for this problem:

`\begin{cases}x+y=20 \\ 5x+2y=46\end{cases}`

We can use the substitution method and clear y from the first equation, replace it into the second equation and solve for x:

`\begin{gathered} x+y=20 \\ y=20-x \end{gathered}`

Replacing into the second equation:

`\begin{gathered} 5x+2y=46 \\ 5x+2(20-x)=46 \\ 5x+40-2x=46 \\ 3x+40=46 \end{gathered}`

And solving for x:

`\begin{gathered} 3x=46-40 \\ 3x=6 \\ x=(6)/(3)=2 \end{gathered}`

Answer:

Ms. Doyle bought 2 pizzas