Question

Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of cheese pizza? Set up the system of equations:Equation 1 Options - 3x + 4y = 12.504y + 3x = 12.503x + 2y = 12.503x + 4y = 8.50Equation 1 Options - 3x + 4y = 8.502x + 3y = 12.503x + 2y = 8.503x + 4y = 12.50

Answer 1

Answer:

Cost of one slice of cheese pizza = $1.50

System of equations;

$\begin{gathered} \text{Equation 1: }3x+4y=12.50 \\ \text{Equation 2: }3x+2y=8.50 \end{gathered}$

Explanation:

Let x represent the cost of one slice of cheese pizza.

Let y represent the cost of one slice of mushroom pizza.

So if Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50, we can express this as;

$3x+4y=12.50\ldots\ldots\ldots\text{.Equation 1}$

And if Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50, we can express this as;

$3x+2y=8.50\ldots\ldots\ldots\ldots......\text{Equation 2}$

We can now solve both equations simultaneously using the elimination method.

Subtracting equation 2 from equation 1, we'll have;

$\begin{gathered} 2y=4 \\ y=\frac{4}{2} \\ y=2 \end{gathered}$

To find x, let's put y = 2 into Equation 1 and solve for x;

$\begin{gathered} 3x+4(2)=12.5 \\ 3x=4.5 \\ x=\frac{4.5}{3} \\ x=1.5 \end{gathered}$

We can see that the cost of one slice of cheese pizza is $1.50.