8.3.3 Ups and Downs

Notepad iconActivity: 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?

Hint symbol

Comment

What was the actual increase in price? What was the initial cost of gas?

Solutions icon

Answer

(a) The actual increase is dollar 3.51 postfix minus dollar 3.25 equals dollar 0.26.

So, the percent increase in gas prices is multiline equation row 1 dollar times 0.26 divided by dollar times 3.25 prefix multiplication of 100 percent equals eight percent row 2 up left arrow row 3 cap o times r times i times g times i times n times a times l cap c times o times s times t.

(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.

Hint symbol

Comment

What was the actual decrease in area? What was the original area occupied by the Amazon Rain Forest?

Solutions icon

Answer

(b) The actual decrease is approximately two comma 700 comma 000 times mi super two minus two comma 100 comma 000 times mi super two equals 600 comma 000 times mi super two.

Thus, the percent decrease in the amount of area covered by the Amazon Rain Forest is:

600 comma 000 mi super two divided by two comma 700 comma 000 mi super two equals 0.222 full stop full stop full stop almost equals 22 percent

(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?

Hint symbol

Comment

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 100 percent prefix plus of three percent equals 103 percent of your original salary. Should your original salary be less than or greater than your new salary?

Solutions icon

Answer

(c) We know that $56,780 is 103% of the original salary. This directly translates to dollar 56 comma 780 equals 103 percent multiplication original salary. 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: dollar times 56 comma 780 division 103 percent multirelation equals dollar times 56 comma 780 divided by 1.03 almost equals dollar times 55 comma 126.

(d) You just purchased a gas grill that was 35% off. The sale price was $312. What was the original cost of the grill?

Hint symbol

Comment

This activity is similar to part (d) as we already know the percent decrease. Since it is a decrease, the sales price $312 represents 100 percent negative 35 percent equals 65 percent of the original price. Should the original cost of the grill be less than or greater than the sale price?

Solutions icon

Answer

(d) We know that $312 is 65% of the original price, which is the same as writing dollar 312 equals 65 percent multiplication original price. 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 dollar times 312 division 65 percent equation sequence equals dollar times 312 divided by 0.65 equals dollar times 480.

8.3.2 Percent Decrease

8.3.4 Fact or Fiction?