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2019 AMC 12A Problem 1

Problem 1 of 25EasierAlgebraGeometry

The area of a pizza with radius 44 inches is NN percent larger than the area of a pizza with radius 33 inches. What is the integer closest to N?N?

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Solution

The areas are proportional to the squares of the radii, so the ratio of the larger area to the smaller is 169.\dfrac{16}{9}. The percent increase is (169−1)×100=7009≈77.8. \left(\dfrac{16}{9} - 1\right) \times 100 = \dfrac{700}{9} \approx 77.8. The closest integer is 78.78. Thus, the correct answer is E.

More practice

Concepts: circle area · percentage

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.