8.3.3 Ups and Downs
Activity: Ups and Downs
(a) Gas prices rose from $3.25 to $3.51 a gallon since last week. What is the percent increase over the week?
What was the actual increase in price? What was the initial cost of gas?
(a) The actual increase is .
So, the percent increase in gas prices is .
(b) The 1981 Encyclopedia Britannica said that the Amazon Rain Forest occupied 2,700,000 square miles. Three decades later, Wolfram Alpha reported its total area to be 2.1 million square miles. Assuming each report was correct at the time of publication, find the percent decrease from 1981 to 2011.
What was the actual decrease in area? What was the original area occupied by the Amazon Rain Forest?
(b) The actual decrease is approximately .
Thus, the percent decrease in the amount of area covered by the Amazon Rain Forest is:
(c) You were just promoted at work and are getting a 3% raise. Congratulations! Your new salary, $56,780, reflects this increase. What was your salary before the raise?
In this exercise, you already know the percent increase; we need to find the original or base salary. If $56,780 includes your raise, then it represents of your original salary. Should your original salary be less than or greater than your new salary?
(c) We know that $56,780 is 103% of the original salary. This directly translates to . To discover your original salary, we need to do the opposite of multiplication by 103%, which would be division by 103%. Thus, your original salary was: .
(d) You just purchased a gas grill that was 35% off. The sale price was $312. What was the original cost of the grill?
This activity is similar to part (d) as we already know the percent decrease. Since it is a decrease, the sales price $312 represents of the original price. Should the original cost of the grill be less than or greater than the sale price?
(d) We know that $312 is 65% of the original price, which is the same as writing . Once again, to discover the original price, we do the opposite of multiplication by 65%, which is division by 65%. Thus, the original cost of the grill is .