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.

To find the percent of change, use the following proportion:

Percent of change: Amount of increase or decrease = % Original Amount  100

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=

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

Try This!

A CD's original price was $12.99. It is now on sale for $10.99.What is the percent of change?

Try This!

A student's first test grade was 60. The second test grade was an 85.What was the percent of change?

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?

39 Original Amount: 500 New: 700 Find the percent of change.

40 Original Amount: 52 New: 17 Find the percent of change.

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?

42 Find the percent of change.Original price: $120Sale price: $75

43 Find the percent of change.Original price: $80Sale price: $50

44 A stereo, originally priced at $360, is on sale for $200. What is the percent of change?

Representing Percent Equations

Algebraically

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.

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

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.

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

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.

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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

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?

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

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?

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

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?