Interpret Equations

Julie is a professional gift-wrapper.  She uses the expression $bp(4hl+2lw)$ to estimate her wrapping paper costs. In the expression $b$ represents the number of boxes she will wrap, $p$ represents the average cost per square foot of the wrapping paper that she uses, $h$ is the average height of her boxes in feet, $l$ is the average length of the boxes in feet, and $w$ is the average width of the box in feet.  

  1. If the cost of Julie's favorite wrapper paper goes up significantly, which variable will change?
  2. During the holidays, Julie wraps many more boxes than she does during the rest of the year. During the holidays, which variable tends to be higher?
  3. Based on the expression, what is the best interpretation of the meaning of the number 4?
  4. Based on the expression, which will have a bigger impact on wrapping paper costs, many boxes with larger heights or many boxes with larger widths?

Garret is trying to create an expression to represent the number of pages of summer reading he has left.  He has come up with $L=3670-64d$ in which $L$ represents the number of pages that Garret has left to read and $d$ represents the days of summer that have passed.

  1. In the expression, what will happen to variable $d$ as the summer progresses?
  2. As $d$ increases, what will happen to $L$?
  3. What is the best interpretation for the meaning of 3670 in the equation?
  4. What is the best interpretation for the meaning of 64 in the equation?

The city lake rents boats to tourists in the summer. A guide book tells visitors that they can use the expression $C=8+5h+3r$ to calculate the cost of their boat rental.  The guide explains that $C$ represents the cost of the boat rental, $h$ represents the hours of the rental, and $r$ represents the number of riders in the boat.

  1. In the expression, what is the best interpretation for the meaning of 5 in the equation?
  2. What is the best interpretation for the meaning of 8 in the expression?
  3. Who will pay more for the boat rental, a group of 8 who rent the boat for 2 hours, or a group of 2 who rents the boat for 8 hours?
  4. Would it be cheaper for a group of 8 to rent one boat for 4 hours or two boats (each with 4 people) for 4 hours?

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