Chapter 2.4, Problem 34E

To determine

To explain: whether the friend is correct or not

Answer to Problem 34E

Friend is almost right

Explanation of Solution

Given:

Forest Park Campgrounds charges a 100$ membership fee plus 35$ per night.

Woodland Campgrounds charges a 20$ membership fee plus 55$ per night.

Statement of friendis s for four or more nights, choose Woodland Campgrounds.

Calculation:

Let's note:

  $x=$ the number of nights in the camping

Write the expression for the cost of $x$ nights in Forest Park Campgrounds:

  $100+35x$

Write the expression for the cost of $x$ nights in Woodland Campgrounds:

  $20+55x$

Study for how many nights Woodland Campgrounds has a better cost:

  $20+55x\ge 100+35x$

  $20+55x-35x\ge 100+35x-35x$

  $20+20x\ge 100$

  $20+20x-20\ge 100-20$

  $20x\ge 80$

  $x\ge 4$

Friend is almost right: for more than 4 nights the Woodland Campgrounds is better, but for exactly 4 nights any of the two camping would do as they charge the same cost.

Therefore, $x\ge 4$

Conclusion:

Therefore, friend is almost right