Help me with this ridiculously difficult question

Question

The grocery store has bulk pecans on sale, which is great since you're planning on making 8 pecan pies for a wedding. How many pounds of pecans should you buy?

How many pecans are needed for each pie? Your recipe calls for 1 1/2 cups pecans per pie. But there is no cup measure available, only a scale.

How many pecans are in a pound? Perhaps the nutritional info from a bag of pecans would be helpful.

Serving Size: 1 cup, halves (99 grams)

Servings per container: about 2

Amount per serving

Calories: 684

Calories from fat: 596

Total fat: 71 grams

Saturated Fat: 6 grams

Trans fat: 0 grams

Cholesterol 0 milligrams

YOU WILL NEED TO BUY HOW MANY POUNDS OF PECANS? GIVE ANSWER TO AT LEAST ONE DECIMAL PLACE!

Answer 1

You are making 8 pies, each of which contains 1.5 cups. Therefore, you need 8 * 1.5 = 12 cups. Unfortunately, you don't have a cup measure, so you will need to convert this result from cups to another unit. Fortunately, the nutritional info indicates that 1 cup (a measure of volume) is 99 grams (a measure of weight). Therefore, 12 cups is 12 * 99 grams. Phew! Now we know how many grams we need. Unfortunately, the question asks for pounds (also a measure of weight). Fortunately, Google tells us that 454 grams (approximately) equals one pound. Now let's write the following fraction: 1 pound / 454 grams. Because the numerator and denominator are equal, the fraction equals 1. Therefore, we can multiply our quantity by this fraction without changing its value. (After all, multiplying anything by 1 does not change its value!) We then get the following expression: 12 * 99 grams * 1 pound / 454 grams. Because grams appear both in the numerator and denominator, they cancel, leaving the following expression: 12 * 99 * 1 pound / 454. The only units left are pounds, which is what we want, and all that is left to do is some simple arithmetic.