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mathcounts problems 1

91. Mrs. Smith’s 1st period class of 28 students averaged 84% on the last test. Her 2nd period class of 24 students averaged 86% on the same test. What must her 3rd period class of 32 students average so that all of the students in her three classes have a combined average of 80%?

93. If 5ab-c=36 and b=c=1/2a, what is the value of a?

94. A bus stopped at Main Street and boarded passengers, after which half of its seats were filled. At its next stop, at Oak Street, 2 passengers got off and 7 got on, and then 60% of the seats were filled. How many seats are there on the bus?

95. Three fractions are inserted between 1/4 and 1/2  so that the five fractions form an arithmetic 

sequence. What is the sum of these three new fractions? Express your answer as a common fraction.

96. In the equation 123 × 4A6 = 5B548, what is the value of A × B, the product of the two missing digits?



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