Averaging Kelly's Test ScoresDate: 01/07/2002 at 19:12:55 From: Brittney Subject: Kelly's test scores Kelly's average score on four Spanish tests is 85.5. The average of her three highest scores is 87, and her two lowest scores are the same as each other. What is the average of her two highest test scores? I am totally stumped. I really need help! Brittney Date: 01/07/2002 at 23:42:26 From: Doctor Pete Subject: Re: Kelly's test scores Hi, Here's the way I went about solving this question. If the average score of her four tests is 85.5, what is the total number of points she received over the four tests? We know it must be 4 x 85.5 = 342 points, since the definition of "average" is the sum of all the scores, divided by the number of tests. In other words, Average = Total / Number, or equivalently, Average x Number = Total. Similarly, we may ask the question "what is the sum of her three highest scores?" We know the average is 87, and there were three such exams, hence the sum is 3 x 87 = 261 points. Since this total does not count her lowest test score, and the previous total of 342 points does count this lowest score, we must conclude that the lowest score is 342 - 261 = 81 points. Since we are also told that her lowest two scores are the same, we see that the total of her highest two scores must be 342 - (2 x 81) = 180 points, and since this is the sum of her two highest scores, the average of these two scores is half, or 90 points. To summarize, we can organize the solution into a table: [Number of Tests] x [Average] = [Sum of Scores] 4 x 85.5 = 342 3 x 87 = 261 ----------------------------------------------- 1(lowest) = 342-261 = 81 2(lowest) x 81 = 162 ----------------------------------------------- 2(highest)x [Average] = 342-162 = 180 As you can see, we don't need algebra to solve this problem - although we could have described the situation using variables for her test scores, it is perhaps simpler to use the fundamental definition of averages to arrive at the correct answer. Also, we should be aware that the problem does not contain enough information to find each score, only the lowest two scores and the average of the top two scores. - Doctor Pete, The Math Forum http://mathforum.org/dr.math/ |
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