Monthly Archives: March 2011

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?

New Application Problems from the Classroom

Here are few more problems that I came up with during today’s class:

1.  Clyde owed 8 different people $4 each for some doughnuts that he bought to eat on his birthday. Then when he wasn’t looking, Hellman’s stole $4 from Clyde’s wallet.  In order to reclaim his debt, Clyde needed to split up his total losses over a period of nine months.  How much debt will he recover over each of the nine months?

2.  Clyde went to the store and he bought seven nuclear weapons, but he doesn’t know the price of them yet.  He had to return four of the weapons because they were defective.  Then Clyde had to pay $9 in order to bribe a government official into letting him keep the weapons.  Finally, when buying the weapons, Clyde had a $4 off coupon.  How much did Clyde pay since he did not yet know the price per weapon?

3.  The hypotenuse of a right triangle is the median of {0.52, 0.69, 0.71, 0.34, 0.54} and one of the legs is the median of {0.26, 0.12, 0.35, 0.43, 0.28}.  Find the length of the missing side.

4.  The length of a boat is the mean of {11, 32, 21, 74, 32, 25, 29} ft.  Convert the length of the boat to meters.

5.  The diameter of a doughnut is the average of {3.6, 7.4, 3.9, 6.2, 7.6} cm.  Convert the diameter to millimeters.