Answer:
14 climbers.
Step-by-step explanation:
Let us assume that the number of climbers in the group is x and the cost per person on the bus is y.
Now, total cost of bus fair = 280 = xy - 0.25x + 12 Â
{Where $12 is the cost of group permit and $0.25 per person is deducted as discount}
⇒xy - 0.25x = 268
⇒ [tex]y=\frac{268}{x} +0.25[/tex]
Now, it is given that y ≤ 20
⇒ [tex]\frac{268}{x} +0.25\leq 20[/tex]
⇒ [tex]\frac{268}{x} \leq 19.75[/tex]
⇒ [tex]\frac{x}{268} \geq  \frac{1}{19.75}[/tex]
⇒ [tex]x\geq  \frac{268}{19.75}[/tex]
⇒ [tex]x\geq13.57[/tex]
Since x can not be a fraction.
Therefore, there must be at least 14 climbers in the group for the cost per person to be $20 or less. (Answer)
