12. A 12”-diameter pizza and a 16”-diameter pizza are each cut into eight congruent slices. Jane ate three slices of the 12”
pizza. Mark ate three slices of the 16” pizza. How many more
square inches of pizza than Jane did Mark eat? Express your
answer as a common fraction in terms of S.

9514 1404 393

  21/2π ≈ 33 square inches

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr^2

In terms of diameter, this is ...

  A = (π/4)d^2 . . . . . . . where r = d/2

Each at 3/8 of the pizza area, so their portion of the circles with diameter d was ...

  serving size = (3/8)(π/4)d^2 = (3π/32)d^2

Then the difference in serving sizes, based on the difference in diameters, is ...

  (3π/32)(16^2 -12^2) = (3π/32)(112) = 21/2π . . . square inches

Mark at (21/2)π square inches more pizza than Jane.

__

That's about 32.99 square inches more.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.