A scooter costs $160.
For each question, show your reasoning.
- The cost of a pair of roller skates is 20% of the cost of the scooter. How much do the roller skates cost?
- A bicycle costs 20% more than the scooter. How much does the bicycle cost?
- A skateboard costs 25% less than the bicycle. How much does the skateboard cost?
14.2: Taxes and Sales
- You need to pay 8% tax on a car that costs $12,000. What will you end up paying in total? Show your reasoning.
- Burritos are on sale for 30% off. Your favorite burrito normally costs $8.50. How much does it cost now? Show your reasoning.
- A pair of shoes that originally cost $79 are on sale for 35% off. Does the expression \(0.65(79)\) represent the sale price of the shoes (in dollars)? Explain your reasoning.
Come up with some strategies for mentally adding 15% to the total cost of an item.
14.3: Expressing Percent Increase and Decrease
Complete the table so that each row has a description and two different expressions that answer the question asked in the description. The second expression should use only multiplication. Be prepared to explain how the two expressions are equivalent.
|description and question||expression 1||expression 2 (using only multiplication)|
|A one-night stay at a hotel in Anaheim, CA costs $160. Hotel room occupancy tax is 15%. What is the total cost of a one-night stay?||\(160 + (0.15)\boldcdot 160\)|
|Teachers receive 30% educators discount at a museum. An adult ticket costs $24. How much would a teacher pay for admission into the museum?||\((0.7)\boldcdot 24\)|
|The population of a city was 842,000 ten years ago. The city now has 2% more people than it had then. What is the population of the city now?|
|After a major hurricane, 46% of the 90,500 households on an island lost their access to electricity. How many households still have electricity?|
|\(754 - (0.21)\boldcdot 754\)|
|Two years ago, the number of students in a school was 150. Last year, the student population increased 8%. This year, it increased about 8% again. What is the number of students this year?|
We can write different expressions to calculate percent increase and decrease.
Suppose a new phone costs \$360 and is on sale at 25% off the regular price. One way to calculate this is to first find 25% of 360, which is 90, and then subtract \$90 from \$360 to get a sale price of \$270. These calculations can be recorded in this way:
\(\displaystyle 360 - (0.25) \boldcdot 360=270\)
Another way to represent this calculation is to notice that subtracting 25% of the cost is equivalent to finding 75% of the cost. Using the distributive property, we know that \(360 - (0.25) \boldcdot 360\) can be rewritten as \((1-0.25) \boldcdot 360\), which is equal to \((0.75) \boldcdot 360\).