Question 567596
Let's try two different ways to solve this problem.
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First, let's look at how many points Gina must score on 5 tests to have an average score of 85. The average score of 85 will come from dividing the total number of points scored by 5 which is the number of tests. Ask yourself, "What number divided by 5 gives an answer of 85?" The answer to that question is 425, and you can prove that by dividing 5 into 425 to see that the answer is truly 85. 
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You can think about this in several ways. If Gina were to score 85 on every one of the 5 tests she would score 5 times 85 = 425 points and because she scored 85 on every test, her average score would be 85. That tells you that 425 points is the total that Gina needs to score on the five tests. You could also set up an equation that says the unknown number of total points needed is X and when you divide by the total number of tests (5) the answer needs to be 85. This equation would be:
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{{{X/5 = 85}}}
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and you would multiply both sides by 5 to get rid of the denominator on the left side. This multiplication would result in:
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{{{(5*X)/5 = 5*85}}}
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on the left side the 5 in the numerator cancels with the 5 in the denominator and the left side of the equation becomes just X. On the right side of the equation multiply 5 times 85 and you get 425.
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So now we know that Gina must score a total of 425 points on the 5 tests. The problem tells you that on the first 4 tests her scores were 83, 86, 79, and 80. Add these 4 scores together and you get 328. You know that she needs a total of 425 points on 5 tests, so all the remaining points must be scored on the fifth test. Subtract the 328 points that she currently has from the 425 points she needs, and you find that the points she needs on the fifth test are 97. That's the answer. Gina needs a grade of 97 on the fifth test in order to average 85 on the 5 tests.
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There's another way you can solve this problem. Remember that we said if Gina scored 85 on every test she would have an average score of 85 for all 5 tests? Well, let's use that fact to solve the problem. On the first test she scored 83 points. That's 2 points below what she would need to get 85. Let's indicate this by -2. On the second test she scored 86 points. That's 1 point above what she would need to get 85. Let's indicate this by +1. On the third test she scored 79 which is 6 points below 85. Call this -6. And on the fourth test she scored 80 which is -5 points below 85. Add up these 4 plus and minus scores as follows:
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{{{-2 + 1 -6 - 5 = -12}}}
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So going into the fifth test Gina is 12 points below what she needs to get. But we assumed she would get an 85 on the last test (just as she needed to do on all 5 tests). So on the last test she needs to score 85 plus 12 extra points to make up for her lower grades on the first 4 tests, and this is a total of 97 points, just as we found by the first method.
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In summary, the answer to the question is that Gina needs to score 97 points on the last test.
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I hope this helps you to understand the problem a little better and you can understand several ways that it (or other problems like it) can be solved.
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