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Problem-Solving and Data Analysis Difficulty: Hard

	Masses (kilograms)
Andrew	2.4	2.5	3.6	3.1	2.5	2.7
Maria	x	3.1	2.7	2.9	3.3	2.8

Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of x ?

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Explanation

The correct answer is 2.6. Since the mean of a set of numbers can be found by adding the numbers together and dividing by how many numbers there are in the set, the mean mass, in kilograms, of the rocks Andrew collected is $the fraction with numerator 2 point 4, plus 2 point 5, plus 3 point 6, plus 3 point 1, plus 2 point 5, plus 2 point 7, and denominator 6, equals 16 point 8 over 6.$ , or 2.8. Since the mean mass of the rocks Maria collected is 0.1 kilogram greater than the mean mass of rocks Andrew collected, the mean mass of the rocks Maria collected is $2 point 8, plus 0 point 1, equals 2 point 9$ kilograms. The value of x can be found by writing an equation for finding the mean: $the fraction with numerator x plus 3 point 1, plus 2 point 7, plus 2 point 9, plus 3 point 3, plus 2 point 8, and denominator 6, equals 2 point 9$ . Solving this equation gives $x equals 2 point 6$ . Note that 2.6 and 13/5 are examples of ways to enter a correct answer.