Question

The cost for a group of climbers to take a bus to a trailhead is $280. The group permit costs $12, minus $0.25 per member bocause the climbers are frequent users. How many climbers must be in the group for the cost per person to be $20 or less?

Answer 1

14 climbers.

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

{Where $12 is the cost of group permit and $0.25 per person is deducted as discount}

⇒xy - 0.25x = 268

⇒
`y=(268)/(x) +0.25`

Now, it is given that y ≤ 20

⇒
`(268)/(x) +0.25\leq 20`

⇒
`(268)/(x) \leq 19.75`

⇒
`(x)/(268) \geq  (1)/(19.75)`

⇒
`x\geq  (268)/(19.75)`

⇒
`x\geq13.57`

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)