percent of change day 3
DESCRIPTION
Percent of Change Day 3. Percent of Change: The ratio of the amount of increase or decrease to the original amount It is an increase when the new amount is larger than the original and a decrease when the new amount is smaller than the original. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/1.jpg)
Percent of Change
Day 3
![Page 2: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/2.jpg)
Percent of Change: The ratio of the amount of increase or decrease to the original amount
It is an increase when the new amount is larger than the original and a decrease when the new amount is smaller than the original.
To find the percent of change, use the following proportion:
Percent of change: Amount of increase or decrease = % Original Amount 100
![Page 3: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/3.jpg)
Find the percent of change (be sure to label your answer as an increase or decrease).
Examples:Original amount: 20 Original amount: 40New amount: 30 New amount: 10 Percent of change= Percent of change=
![Page 4: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/4.jpg)
Identify the percent of change as an increase or decrease. Then find the percent of change.
1. Original: 45 New: 75
2. Original: 100 New: 42
3. Original: 58 New: 75
![Page 5: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/5.jpg)
Try This!
A CD's original price was $12.99. It is now on sale for $10.99.What is the percent of change?
![Page 6: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/6.jpg)
Try This!
A student's first test grade was 60. The second test grade was an 85.What was the percent of change?
![Page 7: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/7.jpg)
38 In 2005, the price of a McDonald's hamburger was $0.89. In 2010, the price of a McDonald's hamburger was $1.19. What was the percent of change?
![Page 8: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/8.jpg)
39 Original Amount: 500 New: 700 Find the percent of change.
![Page 9: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/9.jpg)
40 Original Amount: 52 New: 17 Find the percent of change.
![Page 10: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/10.jpg)
41 The number of students who attended FHS in 2010 was 1405. In 2011, 1380 students attended FHS. What was the percent of change in student enrollment?
![Page 11: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/11.jpg)
42 Find the percent of change.Original price: $120Sale price: $75
![Page 12: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/12.jpg)
43 Find the percent of change.Original price: $80Sale price: $50
![Page 13: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/13.jpg)
44 A stereo, originally priced at $360, is on sale for $200. What is the percent of change?
![Page 14: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/14.jpg)
Representing Percent Equations
Algebraically
![Page 15: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/15.jpg)
You have already begun translating percent problems into equations.
Remember...
To solve a percent problem, translate the words into an equation.
Change:1. Percent into a decimal2. "is" to "="3. "of" to " "4. Unknown to "x"
Then, solve the equation.
![Page 16: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/16.jpg)
Think about this...
100% + 5% = 105%
What does that equation look like in decimal form?
1 + 0.05 = 1.05
So, if you increase the price of a shirt 5%, the new price is 105% of the original price. To represent that algebraically, you would write it this way:
Let s = the original price of the shirt
1s + 0.05s = 1.05s
![Page 17: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/17.jpg)
Example:
You sell a shirt for $15.50. This price represents a 5% increase from the price you paid for the shirt. How much did it cost you to purchase the shirt?
Let s = the original price of the shirt
1s + 0.05s = 15.501.05s = 15.50s = $14.76
The shirt cost you $14.76.
![Page 18: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/18.jpg)
Example:
The population of your school decreased by 13% from last year to this year. If there are 957 students in the school this year, how many were there last year?
2 students solved this differently. Who is correct? Why?Is one method easier than the other?
Student 1: Student 2:100% - 13% = 87% 1n - .13n = 95787% of what is 957? 0.87n = 9570.87n = 957 n = 1,100 studentsn = 1,100 students
![Page 19: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/19.jpg)
So, what does this mean?
m + 0.15m = 1.15m
This could mean increase m by 15% or multiply m by 1.15.
They mean the same thing!
Likewise, what is the meaning of
w - 0.42w = 0.58w
This means both decrease w by 42% or multiply w by 0.58.
Click
Click
![Page 20: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/20.jpg)
You Try.
1. A smart phone is on sale for $299, or 18% off. What was the original price of the phone? Write and solve an equation to represent this situation.
2. What does this equation mean? p + 0.02p = 1.02p
3. What does this equation mean? h - 0.1h = 0.9h
![Page 21: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/21.jpg)
45 Write an equation to represent the problem, then solve. Be prepared to show me your equation!
When you go shopping, you must pay an additional 6% in sales tax. What is the price of your items before taxes if your final price is $25?
![Page 22: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/22.jpg)
46 Choose the equation that represents the situation.
The population of a town increased by 1%.
A x + 0.01x = 1.01xB x + 0.1x = 1.1xC x - 0.1x = 0.9xD x - 0.01x = 0.99x
![Page 23: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/23.jpg)
47 Write an equation to represent the problem, then solve. Be prepared to show me your equation!
The number of students in your class has decreased by 12% since September. How many students were there at the start if there are currently 19 students?
![Page 24: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/24.jpg)
48 Choose the equation that represents the situation.
A 15% discount.
A x + 0.15x = 0.85xB x + 1.5x = 2.5xC x - 0.015x = 0.985xD x - 0.15x = 0.85x
![Page 25: Percent of Change Day 3](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56815b5a550346895dc9426b/html5/thumbnails/25.jpg)
49 Write an equation to represent the problem, then solve. Be prepared to show me your equation!
When you paid your bill at a restaurant, you included 24% more to cover tax and tip. If you paid $55.80, what was the amount of the original bill?