17. Paying taxes according to law is an obligation of every citizen. The "Individual Income Tax Law of the People's Republic of China" stipulates that citizens whose monthly salary and wage income does not exceed 800 yuan do not need to pay taxes; the part exceeding 800 yuan is the taxable income for the whole month, and taxes should be paid according to different rates based on the amount exceeding 800 yuan. The detailed tax rates are as follows:
\begin{tabular}{|c|c|c|}
\hline Level & Monthly Taxable Income & Tax (\%) \\
\hline 1 & Up to 500 yuan & 5 \\
\hline 2 & Over 500 yuan to 2000 yuan & 10 \\
\hline 3 & Over 2000 yuan to 5000 yuan & 15 \\
\hline$\cdots$ & $\cdots .$. & $\cdots .$. \\
\hline
\end{tabular}
(1) A citizen's total income in October 2000 was 1350 yuan. How much tax should he pay?
(2) Let $x$ represent the monthly income (unit: yuan), and $y$ represent the tax to be paid (unit: yuan). When $1300 \leqslant x \leqslant 2800$, please derive the function relationship of $y$ with respect to $x$;
(3) An employee of a company paid 55 yuan in taxes in November 2000. What was his total income for that month?
17. (1) In the citizen's income of 1350 yuan in October, the taxable part is 550 yuan. According to the tax rate table, he should pay $500 \times 5\% + 50 \times 10\% = 25 + 5 = 30$ (yuan).
(2) When $1300 < x \leqslant 2800$, 800 yuan is not taxable, and the taxable part is between 500 yuan and 2000 yuan. Among this, 500 yuan is taxed at $5\%$, with a tax of $500 \times 5\% = 25$ (yuan). The remaining part is taxed at $10\%$, so we have
$$
\begin{aligned}
y & =[(x-800)-500] \times 10\% + 500 \times 5\% \\
& =(x-1300) \times 10\% + 25 .
\end{aligned}
$$
(3) According to part (2), when the income is between 1300 yuan and 2800 yuan, the tax amount is between 25 yuan and 175 yuan. Therefore, if an employee of the company pays 55 yuan in taxes, his income must be between 1300 yuan and 2800 yuan. Using equation (1) and setting $y=55$, we get $x=1600$ (yuan).