Tourists

Tourists hire a guide. Everyone will pay the same amount. If there are two fewer of them, they will pay 14 crowns more, and if there are three more, they will pay 14 crowns less. How many tourists are there and how much have the guides paid?

Correct answer:

n =  12
p =  840

Step-by-step explanation:

$$\begin{gathered} (n-2)\cdot (c+14)=p \\ (n+3)\cdot (c-14)=p \\ n\cdot c=p \\ (n-2)\cdot (c+14)=n\cdot c \\ (n+3)\cdot (c-14)=n\cdot c \\ -2\cdot (c-7\cdot n+14)=0 \\ 3c-14\cdot n-42=0 \\ -2\cdot (c-7\cdot n+14)=0 \\ 3\cdot c-14\cdot n-42=0 \\ 2c-14n=-28 \\ 3c-14n=42 \\ Pivot:Row1\leftrightarrow Row2 \\ 3c-14n=42 \\ 2c-14n=-28 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 3c-14n=42 \\ -4.67n=-56 \\ n=\frac{-56}{-4.66666667}=12 \\ c=\frac{42+14n}{3}=\frac{42+14\cdot 12}{3}=70 \\ c=70 \\ n=12 \end{gathered}$$

$p=n\cdot c=12\cdot 70=840$

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