5-B-1: The Magic of Proportions

Problem 1: Tiffany goes to the store to buy a shirt. The shirt’s original coast is $20.00. Today there is a sale of 30 % on all items in the store. How much will Tiffany need to pay to buy the shirt today?

Solution #1 (Proportion): You can solve this problem by using a proportion. Thirty percent can be written as 30/100. Since 100 % of the original price is $20, that needs to go in the denominator of the other fraction. Now, 30/100 = x/20. To solve this proportion, take 30 times 20, which equals 600. Then, take 600 divided by 100, which equals 6. Tiffany does not pay $6 for the shirt, but that is the discount on the shirt. Now, take $20 – $6 and Tiffany will need to pay $14 for the shirt.

Solution #2: If the sale is for 30%, that means you need to find 30 % times $20 to find the discount. You need to rewrite the percent as a decimal, and it becomes .30. Take .30 times $20, and the product is $6.00, which represents the discount. Now, take $20 – $6 and Tiffany will need to pay $14 for the shirt.

Problem 2: Greg earned a 32 out of a possible 35 on his most recent quiz. What was his percentage and letter grade?

Solution: Since we need to find Greg’s percentage on the quiz, we are going to use the number 100, because that always goes along with percents. We know he earned a 32/35, so we are going to make a proportion. For this problem 32/35 = x/100. In order to solve proportions, you first multiply the two numbers which are diagonal from each other. In this case, you take 32 times 100, which equals 3200. Then, you divide that product by the number you haven’t used, which is 35. 3200 divided by 35 is 91.43 (rounded to the nearest hundredth in decimal form). Now, we need to decide which letter grade, Greg earned on the quiz. Since 91.43%, does not round up to 92%, Greg earned a B on this quiz.

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