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2010 AMC 10B Problem 4

Problem 4 of 25EasierAlgebraProbability & Statistics

For a real number x,x, define ♡(x)\heartsuit(x) to be the average of xx and x2.x^2. What is the value of the following expression? ♡(1)+♡(2)+♡(3)\heartsuit(1)+\heartsuit(2)+\heartsuit(3)

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Solution

We have ♡(1)=1+122=1, \heartsuit(1) = \dfrac{1 + 1^2}{2} = 1, ♡(2)=2+222=3, \heartsuit(2) = \dfrac{2 + 2^2}{2} = 3, and ♡(3)=3+322=6. \heartsuit(3) = \dfrac{3 + 3^2}{2} = 6. Then 1+3+6=10. 1 + 3 + 6 = 10. Thus, C is the correct answer.
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