At the end of a school year, the 7th grade teachers came to a meeting with a specified number of parents, where a total of $31$ people have participated.
Sixteen parents of students put questions to the Latin teacher, with the German teacher spoke $17$, with the English teacher $18$, etc., til to the teacher of mathematics, to which all present parents turned.
How many were they exactly?
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When it is said "Sixteen parents" is it meant $16$ people or $16$ couples ans do $32$ people?
Since there is a total number of $31$ people that participated, I suppose that it is meant $16$ people. Is that correct?
Could you give me a hint how we could solve the above problem? I haven't really understood what we looking for. Do we want to determine the number of teacher? Then since we have successive numbers of people at each teacher, do we have $31-16+1$ teacher?
Or have I understood the problem wrong?
Let $P$ be the number of parents and $T$ be the number of teachers. Call the parents the teachers spoke to $s_1, s_2, \dots s_T$
$$P + T = 31$$
$$\begin{array} {rcll} s_1 &=& 16 \\ s_2 &=& 17 \\ &\vdots& \\ s_T &=& 16 + T - 1 &= P \end{array}$$
Can you finish?