[ Arithmetic. Mental arithmetic, etc.]

A hundred people answered the question "Will the new president be better than the previous one?". Of them, a people think it will be better, b - that it will be the same, and c - that it will be worse. Sociologists constructed two "optimism" indicators of the respondents: m=a+b/2 and n=a-c. It turned out that m=40. Find $n$.

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The magnitude of a-c is linearly expressed through $\mathrm{a}+\mathrm{b} / 2$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}$.

## Solution

It is known that $\mathrm{a}+\mathrm{b}+\mathrm{c}=100 ; \mathrm{a}+\mathrm{b} / 2=40$. From the second equation, we get: $2 \mathrm{a}+\mathrm{b}=80$. Subtracting the first equation from the last, we get: a-c=-20, which is what we need to find.

## Answer

$-20$