Mathew needs to get a perfect score of 100 twice for his English test in this year so as to improve on his average score for the whole year from 84 to 86. How many English tests are there altogether in this year?
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If n is the total number of tests in the year, then n-2 is the number of tests before the two having scores of 100 each. The total of scores is found by multiplying the average score by the number of tests. So since the average was 84, the total of the scores was 84(n-2)=84n-168.

We need to add 2×100=200 to this score: 84n-168+200=84n+32, and we know the total score must be 86n:

84n+32=86n, 32=2n, so n=16 tests in the year.

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