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2015 AMC 12B Problem 3

Problem 3 of 25EasierNumber Theory

Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100,100, and one of the numbers is 28.28. What is the other number?

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Solution

Write 2x+3y=100.2x + 3y = 100. If 2828 were written twice, then 3y=100−56=44,3y = 100 - 56 = 44, which is not a multiple of 3.3. So 2828 is written three times: 2x=100−84=16,2x = 100 - 84 = 16, giving x=8.x = 8. Thus, the correct answer is A.
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Tagged: Diophantine Equation · divisibility

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