Homework #11 (due Monday, 4/21):

1. If a recipe calls for 3 tablespoons of cocoa powder for each 2 cups of milk, and you have 7 tablespoons of cocoa powder, how much hot cocoa can you make?

2. Its 1.5 miles from your house to the center of town, and on a map, it appears as 5 inches. What is the scale of the map?

3. If 25% of the people who watch a show watch the commercials, and 35,000 people saw a given commercial, how many people were watching the show total?

4. A plane starts with 50 gallons of fuel, and 3 hours later has 15 gallons of fuel. When will it run out of fuel? Also represent your solution graphically.

5. Cookie A costs $300 for the first 1,000, and costs $40 less for each additional 1,000. Cookie B costs $250 for the first 500, and costs $22 less for each additional 500. Which cookie is more expensive? Give a representation of the information using lines.

6. Make up a problem that requires students to think proportionally (solutions use ratios, fractions, scaling, etc.).

7. Make up a problem that is described by a line: y = mx + b, where b is not zero.

8. Give a written explanation of how the cross-multiply algorithm works, and why. (A reminder: it's not an English assignment, and if an equation or example illustrates some point better than saying it in words, use it. Forget grammatical correctness: make your description as clear as possible.)

9. Critique the following proof of the cross-multiply algorithm. Does it prove that it works? Does it do a good job of explaining it? Do you think it is appropriate for students who are just learning the cross-multiply algorithm? (If not, your answer to the previous question should provide an alternative.)
   
   Consider the quantity a/b. If we multiply the numerator and denominator by a third number d, we obtain an equivalent fraction:
   ad/bd
   Similarly, if we consider c/d, and multiply numerator and denominator by b, we obtain
   bc/bd
   Therefore the following are all equivalent:
   a/b = c/d,
   ad/bd = bc/bd,
   ad = bc.

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