Question

Casey orders 3 pizzas and 2 orders of bread sticks for a total of $42.00. Rachel orders 2 pizzas and 1 order of bread sticks for a total of $26.00. How much does an order of bread sticks cost?

Answer 1

Let "x" represent the cost of one pizza and "y" represent the cost of one bread stick order.

Casey: ordered 3 pizzas and 2 orders of bread sticks for a total of $42

You can express the total cost of her order as an equation

$3x+2y=42$

Rachel ordered 2 pizzas and 1 order of bread sticks for a total of $26, the equation that expresses her total cost is

$2x+y=26$

With this we have established an equation system with two variables.

Rewrite the second equation in terms of y

$\begin{gathered} 2x+y=26 \\ y=26-2x \end{gathered}$

Replace the result in the first equation

$\begin{gathered} 3x+2y=42 \\ 3x+2(26-2x)=42 \end{gathered}$

Solve for x

$\begin{gathered} 3x+2\cdot26-2\cdot2x=42 \\ 3x+52-4x=42 \\ 3x-4x=42-52 \\ -x=-10 \\ x=10 \end{gathered}$

x=$10 now that we know the value of x, we can calculate the value of y as:

$\begin{gathered} y=26-2x \\ y=26-2\cdot10 \\ y=26-20 \\ y=6 \end{gathered}$

y=$6

This means that each order of bread sticks costs $6