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# Pizza problem...

#1
+85817
+10

Pete Zarilla sells 10 inch pizzas for \$4.30, 12 inch pizzas for \$5.88, and 14 inch pizzas for \$7.78. Assume that the price is a quadratic function of the diameter.

We have this set of equations

a(10)^2 + b(10) + c = 4.30   → 100a + 10b + c = 4.30      (1)

a(12)^2 + b(12) + c = 5.88   → 144a + 12b + c = 5.88      (2)

a(14)^2 + b(14) +c  = 7.78   → 196a + 14b + c = 7.78      (3)

Subtract  (1) from (2)   and (2) from (3)    so we have

44a + 2b = 1.58     (4)

52a + 2b = 1.90     (5)

Subtract  (4) from (5)   and we have that 8a = .32 → a = .04

And using (5), we have 52(.04) +2b = 1.90 → b = -.09

And using (1) we have

100(.04) + 10(-.09) + c = 4.30  → c = 1.2

So, our function is

P(d) = (.04)d^2 - .09d + 1.2

Here's the graph using "x" for d..........https://www.desmos.com/calculator/iuv83m3xfc

The price for a 5 inch pizza is 1.75

And using the graph, a \$20 pizza would have a diameter of about 22.84 inches

I believe that the price-intercept being greater than 0 must represent some sort of "fixed charge" of \$1.20, regardless of the size ordered.....

CPhill  Jan 23, 2015
Sort:

#1
+85817
+10

Pete Zarilla sells 10 inch pizzas for \$4.30, 12 inch pizzas for \$5.88, and 14 inch pizzas for \$7.78. Assume that the price is a quadratic function of the diameter.

We have this set of equations

a(10)^2 + b(10) + c = 4.30   → 100a + 10b + c = 4.30      (1)

a(12)^2 + b(12) + c = 5.88   → 144a + 12b + c = 5.88      (2)

a(14)^2 + b(14) +c  = 7.78   → 196a + 14b + c = 7.78      (3)

Subtract  (1) from (2)   and (2) from (3)    so we have

44a + 2b = 1.58     (4)

52a + 2b = 1.90     (5)

Subtract  (4) from (5)   and we have that 8a = .32 → a = .04

And using (5), we have 52(.04) +2b = 1.90 → b = -.09

And using (1) we have

100(.04) + 10(-.09) + c = 4.30  → c = 1.2

So, our function is

P(d) = (.04)d^2 - .09d + 1.2

Here's the graph using "x" for d..........https://www.desmos.com/calculator/iuv83m3xfc

The price for a 5 inch pizza is 1.75

And using the graph, a \$20 pizza would have a diameter of about 22.84 inches

I believe that the price-intercept being greater than 0 must represent some sort of "fixed charge" of \$1.20, regardless of the size ordered.....

CPhill  Jan 23, 2015
#2
+92221
0

This one looks interesting Chris

Melody  Jan 23, 2015

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