Final answer:
The value of a slice that is all pepperoni is found by assigning variables to the value Corey places on veggie and pepperoni pizza, using the ratio of his preference, and factoring in the number of slices. By setting up an equation and substituting values, we calculate that a slice that is all pepperoni is valued at $0.875.
Step-by-step explanation:
To determine the value of a slice that is all pepperoni, we first need to understand the prices Corey and Catherine place on each type of pizza based on Corey's preference for veggies over pepperoni.
Given that the pizza costs $14 and is cut into 8 slices, the price per slice is $14/8, which equals $1.75 for each of the 8 slices. If Corey likes the veggie three times as much as the pepperoni, we can assume that Corey values a slice of veggie pizza three times more than a slice of pepperoni pizza.
Let v be the value Corey places on a slice of veggie pizza, and p be the value he places on a slice of pepperoni pizza. According to Corey's preference, v = 3p. Given that half the pizza is veggie and half is pepperoni, four slices are veggie and four are pepperoni. The combined value of all slices is 8 x $1.75 = $14.
To find the values, we set up the equation: 4v + 4p = $14. Because v = 3p, we substitute to get 4(3p) + 4p = $14, which simplifies to 12p + 4p = $14, leading to 16p = $14. Dividing both sides by 16 gives us p = $14/16, or p = $0.875.
Therefore, the value of a slice that is all pepperoni is $0.875.