# Math test

In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?

Result

J =  40

#### Solution:

$84 = 5a + 3b + 2c \ \\ 25 = a+b+c \ \\ a>0;b>0;c>0 \ \\ 3x = a \ \\ \ \\ a = 6 \ \\ b = 16 \ \\ c = 3 \ \\ \ \\ J = 5 \cdot \ a/3 + 3 \cdot \ b/2 + 2 \cdot \ c = 5 \cdot \ 6/3 + 3 \cdot \ 16/2 + 2 \cdot \ 3 = 40$

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