Jim and Paula jointly purchase the half sausage-half veggie pizza for $21. Suppose that Paula values veggie pizza three times as much as she values sausage pizza. Find the dollar value to Paula of each of the following pieces of pizza:
a. The veggie half of the pizza
b. The sausage half of the pizza
V = Paula's value of veggie portion.
S = Paula's value of sausage portion
V + S = 21
V = 3S
4S = 21
(b) S = $5.25
(a) V = 15.75
To find the dollar value to Paula of each piece of pizza, we need to set up a system of equations based on the given information. Let's define the value of the veggie half of the pizza as V and the value of the sausage half of the pizza as S.
According to the problem, Paula values the veggie pizza three times as much as the sausage pizza. This can be expressed as:
V = 3S (Equation 1)
We also know that when Jim and Paula jointly purchase the half sausage-half veggie pizza, they pay $21. Therefore, we can express the total value of the pizza as:
V + S = $21 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (V and S) that we can solve simultaneously.
First, let's solve Equation 1 for V:
V = 3S
Now substitute this expression for V into Equation 2:
3S + S = $21
Combine like terms:
4S = $21
Divide both sides by 4:
S = $5.25
Now substitute the value of S back into Equation 1 to find V:
V = 3(5.25)
V = $15.75
Therefore, the dollar value to Paula of each piece of pizza is:
a. The veggie half of the pizza is valued at $15.75
b. The sausage half of the pizza is valued at $5.25