Question

at the soccer game last weekend Dave bought three slices of pizza and two bottles of water for $12.75 at the same concession stand Angie bought one slice of pizza and three bottles of water for 7.75. what is the price of each item at the concession stand​

Answer 1

Let's start by converting this word problem into math equations... This will make it much easier to choose an approach to the problem!

Write equations for both Dave and Angie. We will use the variables P for slices of pizza, and W for bottles of water bought.

(1) Dave:
`3P+2B=12.75`

(2) Angie:
`1P+3B=7.75`

Now that we have these equations, it's much easier to tell that this is a system of two equations (two equations, two unknowns). To solve this system, we can use a variety of different methods. For this problem, let's use the Elimination method (removing one variable from the equation.

Start by multiplying (scaling) Angie's equation by a factor of -3, so that we will be able to remove Pizza slices from the equation:

(3)
`-3(1P+3B=7.75) \equiv -3P-9B=-23.25`

Now, let's add Angie's new equation to Dave's original:

`-7B=-10.5`

Notice that we now only have one variable in this simple equation. This is very easy to solve!

Simplify:

`B=1.5`

Now that we have the price for a bottle of water, we can substitute this value into either (1) Dave's or (2) Angie's original equation to find the price for a slice of Pizza (P). I will substitute into (1) Dave's equation:

Substitute:

`3P+2(1.5)=12.75`

Simplify:

`3P=9.75`

Divide:

`P=3.25`

Finally, we have reached our conclusion... A slice of Pizza costs $3.25 and a bottle of water costs $1.5 at the concession stand! Let me know if you have any questions or want to learn other ways of solving this problem!