Question 560279: how do u solve a question that state ; a student has scores of 88, 92, and 86 on first 3 tests. whats score must he get on the forth so her average is 90
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Ask yourself how would you determine the average for four exams.
.
The way you get the average score is to add up the scores on each of the four tests and then divide that total by the number of tests which is 4. But in this problem, you want the average to be 90. So you just reverse the process. You multiply the number of tests, which for this problem is 4, times 90 to get the total score you need. 90 times 4 is 360. So you will need a total of 360 points to average 90 on four tests.
.
That being the case, on the first three tests you have scored 88, 92, and 86 points. Adding those three scores together gives a total of 266 points. On the next test you need to add a score that will get you to 360 points. So you need to get 360 minus 266 points which means you need to score a 94.
.
You can check this answer by finding the average score. Add up the four scores of 88 + 92 + 86 + 94 and you have a total of 360 points. Then divide by 4, the number of tests, and you find that 360 divided by 4 is 90. So the answer checks.
.
That is probably the easiest way to understand how to get the answer. But here's another way you could do the problem.
.
You want your average to be 90. On the first test you scored 88. That is 2 points less than you need to average 90. So you are down 2 points or -2. On the next test you scored 92 and that is 2 points more than 90 so you have +2 points for that exam. And on the third test you scored 86 points. That is 4 points less than 90 so you have -4 points. Now add up the three differences:
.
-2 +2 -4 = -4
.
This tells you you are down a total of 4 points below 90, and to make that up on the fourth test you need to score 4 more than 90 so you need to score 90 + 4 or 94 points. This is the same answer that we got using the other method.
.
In summary, the answer to this problem is you need to score 94 on the fourth test to average 90.
.
For practice of this second method, let's assume that you have made the same three scores on the first three tests (88, 92, and 86. What would you need to score on the fourth test to have an average grade of 91? On the first test you scored 88 which is -3 points below 91. On the second grade you scored 92 points for +1 point above 91. On the third test you scored 86 points or -5 points from 91. Add these three results:
.
-3 + 1 -5 = -7
.
So you are 7 points below what you need to average 91. That means that on the fourth exam you need to score 91 + 7 points or a total of 98 points to make up the difference and have a 91 average on the 4 tests.
.
You can quickly check this answer using the first method. To average 91 on 4 tests, you need a total of 4 times 91 points which means you need 364 points. Recall that on the first 3 tests, you scored 88 + 92 + 86 which is 266 points. So on the fourth exam you need to score 354 - 266 = 98 points to average 91. This is the same answer, just a different way of getting it.
.
I hope this helps you to a better understanding of working with averages.
.
|
|
|
