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555-605 (Medium)|   Geometry|         
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Bunuel
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 28 Jan 2015, 07:47
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C
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79% (02:12) correct 21% (02:18) wrong based on 300 sessions

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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill ate 2/5 of the pizza; Ted ate 1/4. If there are 3 and a half slices left over, what was the area, in square inches, of each individual slice?

A. 2π
B. 5π
C. 10π
D. 20π
E. 40π

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C
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 28 Jan 2015, 10:49
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Since diameter = 20 radius =10 .

Total area = 100 pai.
Out of which
Bill ate 40 pai. T at e 25 Pai.

Rest is 35 Pai.

Left over =3.5 slices.
If area is 10pai then 3and a half slices will be left.

So ans : 10 Pai
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 28 Jan 2015, 08:38
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ans C 10pi...
total pizza eaten 13/20... so remaining 7/20=7/2 slices..
total slices = 10..
area of each slice=1/10 of entire pizza
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 28 Jan 2015, 21:38
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Given diameter=20
radius=10
area of pizaa=100 pi

bill had 2/5 of pizza=40 pi
Ted had 1/4th of pizza=25pi
remaining=100 pi-65 pi=35pi
3.5 number of slices remaining=35 pi
area of each slice=35 pi/3.5=10pi

Answer is C
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 02 Feb 2015, 03:24
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Bunuel
Bill and Ted split an excellent pizza with a 20-inch diameter. Bill ate 2/5 of the pizza; Ted ate 1/4. If there are 3 and a half slices left over, what was the area, in square inches, of each individual slice?

A. 2π
B. 5π
C. 10π
D. 20π
E. 40π

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VERITAS PREP OFFICIAL SOLUTION:

Answer: (C)

This is a two-step problem: if you want to solve for the area of each slice, you first need to know how many slices there are in one whole pizza. If Bill ate 2/5 of the pizza and Ted ate 1/4, their combined fraction (adding them with the least common denominator of 20) of 13/20 represents the portion of the pizza eaten. The 3.5 left over slices therefore are the remaining 7/20 of the pizza. You can set up a simple ratio to solve for the total number of slices (or just logic it out): 7/20= 3.5/total . Cross-multiply to get 7(total) = 3.5(20), and solving for the total you get 10.

Once you’ve determined there are 10 slices in a full pizza, the area of each slice is just one-tenth of the total area. We were given the diameter (20 inches), from which we can solve for radius (10) and area (π∗10^2=100π). Dividing this total area by ten slices, you get an area of 10π per slice.
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 03 Feb 2015, 21:28
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Excellent pizza area \(= 100\pi\)

Left over \(= 100\pi - (100\pi*\frac{2}{5} + 100\pi*\frac{1}{4}) = 35\pi\)

Let size of each piece = x

Given that \(3.5x = 35\pi\)

x = \(10\pi\)

Answer = C
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 10 Apr 2017, 14:11
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r=10
area=100pi
B ate 2/5 * 100pi = 40pi
T ate1/4*100pi=25pi
total eaten: 65pi.
left 35pi.

we are left with 7/2 slices.
1 slice is 35pi*2/7=5pi*2 = 10pi.
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Bill and Ted split an excellent pizza with a 20-inch diameter. Bill at 03 Oct 2023, 06:36
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