The average for the first 3 tests is 85, meaning that t1 + t2 + t3 = 3*85.
In order to raise the average by two points, then the average for the four tests must be 87, or t1 + t2 + t3 + t4 = 4*87.
Notice that t4 will be 4*87 - 3*85 = 4*(85 + 2) - 3*85 = 4*85 + 8 - 3*85 = 4*85 - 3*85 + 8 = 85 + 8 = 93.
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Jose Ferreira
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Hi lolo,
Dana is right on. A related way to think about this:
On the fourth test, let's say the score is 85. Then the average across the four tests is 85.
But we want the average score across the four tests to go up by 2 points. So the score on the 4th test has to pick up an additional 2 points for each of the 4 tests. That is, it needs to be 4*2 = 8 points higher. This way, the average score bump per test is 8/4 = 2.
This means that the 4th score must be 85 + 8 = 93.
Dana is right on. A related way to think about this:
On the fourth test, let's say the score is 85. Then the average across the four tests is 85.
But we want the average score across the four tests to go up by 2 points. So the score on the 4th test has to pick up an additional 2 points for each of the 4 tests. That is, it needs to be 4*2 = 8 points higher. This way, the average score bump per test is 8/4 = 2.
This means that the 4th score must be 85 + 8 = 93.
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franciskyle
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You could immediately draw the below equation from the problem - X being the fourth test score.
(3*85 + X)/4 = 87
Therefore X = 93
(3*85 + X)/4 = 87
Therefore X = 93
k. Francis
