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:

$$\begin{gathered} 84=5a+3b+2c \\ 25=a+b+c \\ a>0;b>0;c>0 \\ 3x=a \\ a=6 \\ b=16 \\ c=3 \\ J=5\cdot a\mathrm{/}3+3\cdot b\mathrm{/}2+2\cdot c=5\cdot 6\mathrm{/}3+3\cdot 16\mathrm{/}2+2\cdot 3=40 \end{gathered}$$

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