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2001 AMC 10 Problem 3

Problem 3 of 25EasierAlgebraArithmetic

The sum of two numbers is S.S. Suppose 33 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?

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Solution

Let the numbers be aa and b,b, so a+b=S.a+b=S. After adding 33 to each and doubling, the sum is 2(a+3)2(a+3) +2(b+3)+2(b+3) =2(a+b)+12=2(a+b)+12 =2S+12.=2S+12. Thus, the correct answer is E.
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Tagged: algebraic manipulation · distributive property

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