For each of the following, find the valuations:

a. Chance and Brianna buy a pizza for $16 that is half pepperoni and half veggie. They cut the pizza into 8 slices. If Chance likes veggie three times as much as pepperoni, what would he consider the value of a slice that is half pepperoni, half veggie?

b. Ahmed and Tiana spend $24 on a cake that is half chocolate and half vanilla. They cut it into 6 slices. If Ahmed likes chocolate four times as much as vanilla, what would Ahmed consider the value of a slice that is half chocolate, half vanilla?

a) the value is $2 for that slice

b) the value is $3 for that slice

Step-by-step explanation:

a) Since the pizza costed $16, denoting the value of the slice of pepperoni as P and V as the veggie slice then

4 slices * P + 4 slices * V = $16

if Chance likes 3 times more the veggie than the pepperoni slice, then he finds V three times more valuable than P, thus

V = 3*P

therefore

4 slices * P + 4 slices * 3*P = $16

16 slices * P = $16 → P=$1/slice

V = 3*P = 3*$1/slice = $3/slice

for a slice that is half pepperoni and half veggie

value = 1/2 slice * P + 1/2 slice * V = 1/2 slice ($1/slice + $3/slice) = $2

then the value is $2

b) Similarly to the first case, denoting the value of the slice of chocolate as C and V as the vainilla slice then

3 slices * C + 3 slices * V = $24

if Ahmed likes 4 times more the chocolate than the vainilla slice, then he finds C four times more valuable than V, thus

C = 4*V

therefore

4 slices * 4*V + 4 slices * V = $24

20 slices * P = $24 → P=$1.2/slice

V = 3*P = 4*$1.2/slice = $4.8/slice

for a slice that is half chocolate and half vainilla

value = 1/2 slice * C + 1/2 slice * V = 1/2 slice ($1.2 / slice + $4.8/slice) = $3

then the value is $3