SOLUTION: Angela’s average for six math tests is 87. On her first four tests she had scores of 93, 87, 82, and 86. On her last test, she scored 4 points lower than she did on her fifth

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Question 1182100:
Angela’s average for six math tests is 87. On her first four tests she had scores of 93, 87, 82, and 86. On her last test, she scored 4 points lower than she did on her fifth test. What scores did Angela receive on her fifth and sixth tests?
Found 3 solutions by ikleyn, mananth, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Angela’s average for six math tests is 87. On her first four tests she had scores of 93, 87, 82, and 86.
On her last test, she scored 4 points lower than she did on her fifth test.
What scores did Angela receive on her fifth and sixth tests?
~~~~~~~~~~~~~ 

Let x be her score on her 5the test.

Then the score on her 6th test was (x-4), according to the condition.


Next, you write the equation for the average for six math tests


     = 87.


Simplify and find x


     = 87

    344 + 2x = 6*87

          2x = 6*87 - 344

          2x = 178

           x = 178/2 = 89.


ANSWER.  her score is 89 on her 5th test and 89-4 = 85 on her 6th test.

Solved.

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Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


In problems involving averages of numbers that are close together, I find it faster and easier to solve the problem using an "over/under" strategy, rather than the formal definition of an average.

In this problem, using this strategy makes solving the problem almost trivial, because the average on her first four tests is 87. This is easily seen by looking at the "overs" and "unders" for those tests:
93: +6
87: +0
82: -5
86: -1
total overs and unders on tests 1 to 4: 0

That means the average of her fifth and sixth tests must also be 87. And since her score on her sixth test was 4 points lower than on her fifth, simple logical reasoning tells us her scores on her fifth and sixth tests were 87+2=89 and 87-2=85.

ANSWERS:
5th test 89
6th test 85
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