The number of pepperoni slices that kim puts on a pizza varies directly as the square of the diameter of the pizza. If she puts 15 slices on a 10" diameter pizza, how many slices should she put on a 16" diameter pizza?

Varies directly as the square of the diameter

square means to multiply by itself or x^2

that means

k=x/y

in this case

x=15

y=10^2

k=15/10^2=15/100=3/20

so the new pizza is

k=x/16^2

k=3/20

3/20=x/16^2

evaluate 16^2

3/20=x/256

multiply both sides by 256

768/20=x

384/10=x

38.4=x

she should put about 38 slises

You can make this into a fraction, and then simplify it.

15/10, right?

15/10 = 3/2

Then compare 3/2 to the rest of the equation

3/2 = x/16

2 * 8 = 16

so

3 * 8 = x

x = 24

Kim would put x number of pizza slices on her pizza.

So she would be putting on 24 slices on her pizza.