Question

A 12" pizza costs $8. How much would you charge for a 9" pizza if you wanted to charge the same amount per bite for both pizzas?

Answer 1

the answer I got doesn't seem right I got 4.2

Answer 2

assuming a bite is a standard unit size (for simplicity's sake we'll imagine its 1 sq in), then we need to find a proportion of the areas of the two pizzas, then relate that proportion to the proportion of our prices.
assuming circular pizzas, A = pi*r^2
a 12 in pizza has an area of A = pi * 12^2 = 144pi
a 9 in pizza has an area of A = pi * 9^2 = 81pi

Since the price must be proportional to the area, we can say that:


plugging in our known values,

144pi/81pi = $8/x

we can now solve for x.
first multiply both sides by x:

144pi*x/81pi = 8

then divide out the pi, and divide each side by 144/81

x = 8/(144/81) = 8*81/144 = $4.5