Question 693798: Carol received an 82, 94, and 88 on three Social Studies tests.What did Carol receive on her fourth test if her average on all four tests was 85?
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! We get the average of something by adding its items together and dividing by the number of items represented. For example, let's say we have 4 shoe sizes. These sizes are 8 inches, 9.5 inches, 10 inches and 12 inches. The total number of inches represented is 39.5 inches, which is 8 + 9.5 + 10 + 12. The average of this number is found by dividing it by the number of items represented. In this case, we have 4 shoes represented. So, the average amount of inches represented is 39.5/4, or 9.875 inches.
This problem is similar to the example above. The two differences are that we have a variable to deal with and we are already given the average. We just need to find the value of one of the items. The first three items are given as 82, 94 and 88. The average is 85. So, given the information above in this answer, we know that:
(82 + 94 + 88 + x)/4 = 85.
The x stands for the test score we don't know and that we need to find. We have four tests being represented, so that is why we divide by 4 after adding all of the scores together. Now we just solve for x:
(82 + 94 + 88 + x)/4 = 85.
(264 + x)/4 = 85
264 + x = 340
x = 76.
The fourth test score is 76. Adding this number and the other three together, we get 340, and dividing by 4, we get the average of 85.
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