# 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?

Correct 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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