Math problems of the week: linear equations in reform vs. traditional algebra

1. From "Say it with Symbols," Investigation 4, about 2/3 of the way through the 8th grade Connected Mathematics curriculum:

The school choir is selling boxes of greeting cards to raise money for a trip.  The equation for the profit in dollars, P, in terms of the number of boxes sold, x, is

P = 3x - (100 + 2x).

a. How many boxes must the choir sell to make a $200 profit?  Explain how you found your answer.

b. How many boxes must the choir sell to break even?  Explain how you found your answer.

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2. From "Systems of linear equations and Inequalities," about 2/3 of the way through McDougal and Littel's Algebra 1, a traditional text:

A gold and copper bracelet weighs 238 grams.  The volume of the bracelet is 15 cubic centimeters.  Gold weighs 19.3 grams per cubic centimeter, and copper weighs 9 grams per cubic centimeter.  How many grams of copper are mixed with gold?

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OILF's assessment:

Translating a word problem into an equat! ion is a core skill, and challenge, in algebra.