Rotten Tomatoes, Linear Equations, Ratio and Proportion

This problem came about because I was talking about solving the equation 4x + y = – 14 for y and there was a little confusion about how I could  subtract 4x from – 14.  Although this was really a problem with combining like terms, I figured that now was as good of a time as ever to reinforce the idea of combining like terms.

“Yaletta bought an unknown number of tomatoes at $4 each, but when she got home, she found out that all of the tomatoes were rotten.  In addition, she checked her receipt and realized that the store had charged $14 to carry the tomatoes to the car.  Write an equation to model Yaletta’s total losses.” (as a signed number)

The students seemed to come to the consensus that an appropriate answer would be y = – 4x – 14.

Then I asked these questions as well:
  • What does y represent?
  • What does x represent?
  • What does -4 mean?
  • What does -14 mean?
  • How much would Yaletta lose if she bought 25 tomatoes?  (as a signed number)

What’s even more interesting about this problem for me is that later in the day I was talking about ratio and proportion and so I used this same problem to ask questions such as:

  • Do you think that it’s fair that the $14 dollar charge is fair?  Why or why not?
  • Would it be more appropriate to have a charge proportional to the number of bags of tomatoes carried to the car?
  • What additional information would we need to know in order to make this change to the charge?