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考题13-14 2017 AMC 8

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AMC 8数学竞赛专为8年级及以下的初中学生设计,但近年来的数据显示,越来越多小学4-6年级的考生加入到AMC 8级别的考试行列中,而当这些学生能在成绩中取得“A”类标签,则是对孩子数学天赋的优势证明,不管是对美高申请还是今后在数学领域的发展都极其有利!那么接下来跟随小编来看一下AMC 8的官方真题以及官方解答吧:

Problem 13Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?

SolutionGiven  games, there must be a total of  wins and  losses. Hence,  where  is Kyler´s wins. , so our final answer is

Problem 14Chloe and Zoe are both students in Ms. Demeanor´s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only  of the problems she solved alone, but overall  of her answers were correct. Zoe had correct answers to  of the problems she solved alone. What was Zoe´s overall percentage of correct answers?

Solution 1Let the number of questions that they solved alone be . Let the percentage of problems they correctly solve together be %. As given,

Hence, .

Zoe got  problems right out of . Therefore, Zoe got  percent of the problems correct.

Solution 2Assume the total amount of problems is  per half homework assignment, since we are dealing with percentages, and no values. Then, we know that Chloe got  problems correct by herself, and got  problems correct overall. We also know that Zoe had problems she did alone correct. We can see that the total amount of correct problems Chloe had when Zoe and she did the homework together is , which is the total amount of problems she got correct, subtracted by the number of correct problems she did alone. Therefore Zoe has  problems out of  problems correct. This is  percent.

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