Math Forum - Problem of the Week


The Hispaniola Water Shortage

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Introduction

Your friend, Rodolfo, lives on the island of Hispaniola. When he cooks he must conserve water, because the family's water supply comes from a rain barrel.

A shop in his town has measuring cups for sale but they come in sets, one set with a 3-oz. cup and an 8-oz. cup, and a second set with a 4-oz. cup and a 10-oz. cup, and Rodolfo has just enough money to buy one set. The store manager understands his problem and agrees that he can test different sets before deciding which ones to buy.

Before going back to the store to make his decision, Rodolfo looks through his recipe file and finds that his recipes call for anywhere from 1 to 12 oz. of water.

Rodolfo hopes to figure out which set of measuring cups will minimize the possibility of spilling water, and yet allow him to measure accurately all the amounts that he needs for his recipes.

Simulation 1

First, Rodolfo tries a 3-oz. cup and an 8-oz. cup. Use the simulation (applet) to determine if he can measure the amounts listed in Table 1.

Click To Show Applet Window

A few answers are filled in to get you started. You might want to copy or print out Table 1.

Table 1
oz. Yes No
1    
2    
3    
4    
5    
6    
7 X  
8    
9    
10 X  
11    
12    

Simulation 2

Next, Rodolfo tries a 4-oz. and a 10-oz. cup. Use the simulation (applet) to determine if he can measure the amounts listed in Table 2.

Click To Show Applet Window

A few answers are filled in to get you started. You might want to copy or print out Table 2.

Table 2
oz. Yes No
1    
2    
3    
4    
5    
6    
7   X
8    
9    
10 X  
11    
12    

Questions:

  1. Do you notice any patterns in Table 1? Explain.

  2. Do you notice any patterns in Table 2? Explain.

  3. Compare the patterns in your two tables. Think about the combinations you used. What do you notice about even and odd numbers?

  4. What are your conclusions about the amounts that can (or cannot) be measured using the two different sets of measuring cups?

  5. Which set of cups would you recommend that Rodolfo buy?

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