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

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}`

Step-by-step 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=(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=(4.5)/(3) \\ x=1.5 \end{gathered}`

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