Word Problems

Filling the Freezer

The Math Club meets one day a week after school to do projects and math investigations. They enjoy having an ice cream snack at each meeting. Their project this week is to buy the ice cream they'll be storing in their freezer for their upcoming meetings.

Before they leave for the store they measure the freezer.

The interior of the freezer is 65 cm wide, 45 cm deep, and 35 cm tall.

At the store they measure an ice cream container.
The dimensions of the top of the box are 17.5 cm by 11.6 cm.
The height is 12.2 cm.
One group, the Protractors, figures out how many boxes will fit in the freezer if they place each box with the lid facing up and the 17.5 cm dimension along the front of the freezer.
Another group, the Right Angles, agrees that they'll keep the lids facing upwards (to avoid messes as some of the containers start to get eaten) and they figure out how many boxes will fit if they turn the boxes and have the 11.6 cm dimension along the front of the freezer.

Questions: Which group can fit more ice cream boxes in the freezer?
How much unused space would be left in the freezer if they buy that many boxes?

Extra: Describe a way to fit more whole containers of ice cream in the freezer. How many can you fit?

Building Bouquets

Jana owns and operates an independent flower shop. To help sell more flowers (and cut down on waste), she offers a daily special of bouquets or corsages created from "leftovers" from larger orders. With today's batch of leftovers, Jana decides to try 4 flowers in each bouquet, but she has three extra flowers left. To make pricing easier, she wants the specials to be the same size, so she tries making the bouquets with 7 flowers each... but then there are two flowers left. If she makes bundles of 8 flowers, she has three flowers left. 1. What is the smallest possible number of flowers that Jana has to work with? 2. With the number of flowers determined above, how many bouquets or corsages and of what size can Jana make? Extra: Do you think that Jana would ever have enough leftovers that it wouldn't matter if she chose to make bouquets of 7, 8, or 9 flowers? (Don't forget - Jana doesn't want to waste a single flower.)

Eating Grapes

On Monday Angela ate some grapes.
On Tuesday she was hungrier and ate six more grapes than she ate on Monday.
Each day that week she ate six more grapes than the day before.
After she had eaten her grapes on Friday she had eaten 100 grapes in all.
How many grapes did she eat on Monday?

Extra: If she continues this pattern, on each day eating six more grapes than the day before, on which

Tatianna and the Troll

A little while ago, Idle Ivan visited a Russian bridge troll. Let me remind you of the story: In an old Russian fable Idle Ivan sighed to himself: "Everybody tells me to get a job or I should make a deal with the troll. But I don't expect even he could help me get rich." No sooner had he said this than the troll appeared from under a nearby bridge. "So, you want to make money, Ivan?" asked the troll. Ivan nodded, lazily. "Then, Ivan, all you have to do is cross the bridge. Every time you do, the money in your pocket will double." Ivan headed for the bridge but the troll stopped him. "Since I'm so generous," the troll said craftily," I think you ought to give me a little for my pains. Will you give me eight rubles every time you cross the bridge?" Ivan agreed and quickly crossed the bridge. He put his hand in his pocket. As if by magic he found his money had doubled. So he threw 8 rubles to the troll. He crossed a second time and did the same. On the third crossing, however, his money doubled but he found when he had paid the troll he had nothing left! The troll laughed and vanished. Now Tatianna decides to try her luck. After she crosses the bridge three times she states the following: "Gee! I still have the same amount of money that I had before I met you, Mr. Troll. I'm no richer nor poorer than I was before. Bah! So much for magic bridges and all that stuff!" How much does Tatianna have in her pocket?