Percent Increase and Decrease Word Problems

Summary

This video script offers a comprehensive guide on calculating the percent of change. It explains the formula, which is the new value minus the original value, divided by the original value and multiplied by 100. The script uses various examples, such as changes in gas prices and savings account balances, to demonstrate how to determine whether the change is an increase or decrease. It also covers word problems involving population changes and student dropouts to illustrate the application of the formula in real-world scenarios.

Takeaways

• 📐 The formula for calculating percent of change is: (New Value - Original Value) / Original Value * 100%.
• 🔢 When the New Value is greater than the Original Value, the percent change is a positive number, indicating an increase.
• 🔽 Conversely, when the New Value is less than the Original Value, the percent change is negative, indicating a decrease.
• 💯 The percent change is always expressed as a percentage, showing how much the value has increased or decreased relative to the original.
• 📉 A negative percent change signifies a decrease, while a positive percent change signifies an increase in value.
• 💡 The script provides practical examples, such as changes in gas prices, savings account balances, cat populations, and student enrollment, to illustrate the calculation of percent change.
• 📈 The percent change can be used to measure the relative change in various quantities over time, such as prices, populations, or account balances.
• 💼 In the example of John's savings account, adding money to the account results in a positive percent change, calculated by the formula.
• 🏫 The script also covers how to calculate percent change when there's a decrease in quantity, such as students dropping a course, using the same formula but resulting in a negative value.
• 🌐 The concept of percent change is applicable across different contexts and can be used to analyze data and make comparisons in various fields.

Q & A

What is the formula for calculating the percent of change?

The formula for calculating the percent of change is: (New Value - Original Value) / Original Value * 100%.

How do you interpret a positive percent change?

A positive percent change indicates an increase from the original value to the new value.

What does a negative percent change signify?

A negative percent change signifies a decrease from the original value to the new value.

If a number changes from 30 to 42, what is the percent change?

The percent change is 40%. (42 - 30) / 30 * 100% = 0.4 * 100% = 40%.

What is the percent change when a value increases from 40 to 70?

The percent change is 75%. (70 - 40) / 40 * 100% = 0.75 * 100% = 75%.

How do you calculate the percent change when a value goes from 30 to 55?

The percent change is 83.3%. (55 - 30) / 30 * 100% ≈ 0.833 * 100% = 83.3%.

What is the percent change when the price of gas increases from $2.24 to $2.56?

The percent change is approximately 14.29%. (2.56 - 2.24) / 2.24 * 100% ≈ 0.142857 * 100% = 14.29%.

If John had $2500 in his savings and added $400, what is the percent change in his savings?

The percent change is 16%. (2900 - 2500) / 2500 * 100% = 0.16 * 100% = 16%.

What is the percent change in the population of cats on Island X if it grew from 1500 to 1750?

The percent change is 16.7%. (1750 - 1500) / 1500 * 100% ≈ 0.167 * 100% = 16.7%.

How do you calculate the percent change in the number of students in a chemistry course if 140 students dropped out from 500?

The percent change is -28%. (360 - 500) / 500 * 100% = -0.28 * 100% = -28%.

What is the significance of the sign (positive or negative) in the percent change calculation?

The sign in the percent change calculation indicates whether there has been an increase (positive) or a decrease (negative) in the value.

Outlines

00:00

📈 Understanding Percent of Change

This paragraph introduces the concept of percent of change and its calculation. The formula for calculating percent change is given as (new value - original value) / original value * 100%. The paragraph explains this with an example where a number changes from 30 to 42, resulting in a 40% increase. Another example is provided with numbers 70 and 40, showing a 75% increase. The paragraph further clarifies that a positive result indicates an increase, while a negative result indicates a decrease. It concludes with a real-world scenario of gas prices changing from $2.24 to $2.56, illustrating how to apply the formula to find a 14.29% increase.

05:02

💼 Practical Examples of Percent Change

The second paragraph delves into practical examples to further illustrate the calculation of percent change. It starts with John's savings account, which increases by $400 from $2500, resulting in a 16% increase. Next, it discusses the population of cats on an island, which grows by 250 from 1500, leading to a 16.7% increase. The paragraph also addresses a decrease in students registered for a chemistry course, where 140 students drop out of 500, causing a 28% decrease. Each example is carefully explained, showing how to identify the original and new values and apply the percent change formula to real-life situations.

10:03

📉 Calculating Decrease in Enrollment

The final paragraph focuses on a specific example of a decrease in the number of students in a chemistry course. It explains how to calculate the percent change when the original number of students is 500 and 140 students drop out, leaving 360. The calculation involves subtracting the new value from the original value, dividing by the original value, and multiplying by 100%, which results in a negative 28% change. This example demonstrates how to handle a decrease in values when applying the percent change formula.

Keywords

💡Percent of Change

Percent of change is a statistical measure that indicates the relative change between two values. It is calculated by taking the difference between the new and original values, dividing by the original value, and then multiplying by 100 to get a percentage. This concept is central to the video's theme, as it is used to demonstrate how to calculate the increase or decrease in various contexts such as gas prices, savings accounts, and population changes. For example, the video uses the formula to calculate the percent change in the price of gas from $2.24 to $2.56, resulting in a 14.29% increase.

💡Formula

The formula for calculating percent change is a mathematical expression that the video explains in detail. It is defined as (New Value - Original Value) / Original Value * 100%. This formula is crucial for the video's educational purpose, as it provides a clear method for viewers to follow when determining the percentage of change in any given situation. The video script uses this formula multiple times to solve different examples, such as calculating the percent change in a savings account balance after a deposit.

💡New Value

The new value refers to the updated or current value after a change has occurred. In the context of the video, it is one of the two essential components needed to calculate the percent of change. The video demonstrates how to identify the new value in various scenarios, such as when the price of gas increases to a new amount or when the number of students in a class decreases after some drop out. The new value is always compared to the original value to determine the change.

💡Original Value

The original value is the starting point or the value before any change occurs. It is a fundamental concept in the video, as it serves as the basis for calculating the percent change. The video emphasizes the importance of identifying the original value accurately, whether it's the initial amount of money in a savings account or the beginning population of cats on an island. The original value is used in the formula to determine how much a value has increased or decreased.

💡Increase

An increase in the video refers to a situation where the new value is greater than the original value, resulting in a positive percent change. The concept of increase is used to illustrate growth or improvement in various contexts, such as an increase in the price of gas or an increase in the balance of a savings account. The video provides examples of how to calculate the percent increase, such as when the number of cats on an island grows by 250, resulting in a 16.7% increase.

💡Decrease

A decrease, as explained in the video, occurs when the new value is less than the original value, leading to a negative percent change. This concept is important for understanding reductions or declines in values, such as a decrease in the number of students enrolled in a course. The video demonstrates how to calculate the percent decrease using the formula, as shown when 140 students drop out of a chemistry course, leading to a 28% decrease.

💡Positive Percent Change

A positive percent change indicates an increase from the original value. The video uses this term to describe situations where the new value exceeds the original value, such as when the price of gas or the balance in a savings account goes up. Positive percent change is calculated using the formula and is always represented as a positive number, signifying growth or a favorable change.

💡Negative Percent Change

A negative percent change signifies a decrease from the original value. The video explains that this occurs when the new value is less than the original value, such as when the number of students in a class drops. Negative percent change is calculated using the same formula as positive change, but the result is a negative number, indicating a reduction or an unfavorable change.

💡Word Problems

Word problems in the video are practical scenarios that require the application of the percent change formula to real-life situations. These problems help viewers understand how to use the concept in various contexts, such as calculating the percent change in gas prices or the population of cats on an island. The video presents word problems to demonstrate the practical application of the formula and to reinforce learning through relatable examples.

💡Calculation

Calculation in the video refers to the process of performing mathematical operations to determine the percent change. It involves using the formula, identifying the original and new values, and executing the arithmetic to find the percentage. The video script guides viewers through several calculations, such as calculating the percent change in a savings account after a deposit or the percent change in the number of students in a class after some drop out.

Highlights

Introduction to the concept of percent of change and its calculation.

Explanation of the formula for calculating percent change.

Example calculation: A number changes from 30 to 42, demonstrating a 40% increase.

Clarification that a positive percent change indicates an increase.

Example calculation: A number changes from 70 to 40, illustrating a 75% decrease.

Example calculation: A number changes from 55 to 30, showing an 83.3% increase.

Explanation that a larger new value compared to the original value results in a percent increase.

Example calculation: A decrease from 50 to 40, resulting in a 20% decrease.

Introduction to word problems involving percent change.

Word problem: Calculating the percent change in gas price from $2.24 to $2.56.

Word problem: Calculating the percent change in John's savings account after adding $400 to $2500.

Word problem: Calculating the percent change in the cat population on Island X after an increase of 250 cats.

Word problem: Calculating the percent change in a college chemistry course after 140 students dropped out of 500.

Emphasis on the importance of identifying original and new values in percent change calculations.

Instruction on how to handle negative values in percent change calculations, indicating a decrease.

Transcripts

in this video we're going to talk about

percent of change

and how to calculate it

so the first thing we need to do is talk

about the formula

and here it is

it's basically equal to the new

value minus the original value

divided by

the original value

multiplied by a hundred percent

so for example

let's say if

a number changes from thirty

to forty two

what is the percent change

the new value is 42

the original value is 30

divided by the original times 100

so that's basically what you need to do

so first subtract these two numbers

42 minus 30 is twelve

and if you divide twelve by thirty

that will give you point four

point four times a hundred percent

is

forty percent

now notice that this is positive forty

percent

so because it's positive it represents

a percent increase

here's another example go ahead and

calculate the percent change

for these two numbers

so starting with the first example

the percent change

is going to be equal to the new value

which is 70

minus the original value of 40

divided by the original value times 100

so 70 minus 40 is 30.

and 30 divided by 40 that's the same as

3 divided by 4

that's equal to 0.75

and if you multiply 0.75 by 100

this will give you positive

75

so that represents a percent increase

so let's try the second example

the percent change is going to be the

new value which is 55

minus the original value of 30 divided

by the original value times 100

55 minus 30

is 25

and so we have 25 divided by 30.

now let's get the decimal value of that

so if you type in 25 divided by 30 in

your calculator

you should get

0.83 repeated

and then multiply that by a hundred

percent and that should give you

positive

83.3 percent

so that too represents a percent

increase so anytime this number

is larger than the first one if the new

value exceeds the original value it will

always be a percent increase

this number your percent change has to

be positive

if it's negative

then it's percent decrease and the only

time you'll have that is if the new

value is less than the original value

so let's say if we have 50

decrease into 40.

this is going to be a percent decrease

because the new value is less than the

original value

go ahead and calculate the percent

change

now your answer has to be negative

the new value is 40 the original value

is 50 and then we need to divide it by

the original value and then multiply it

by 100

so 40 minus 50 is negative 10.

negative 10 divided by 50. if we uh type

that in

that's negative 0.2

so if you take the negative point two

and then multiply by a hundred percent

you're going to get negative twenty

percent

and so that represents a percent

decrease

let's try some word problems

in 2017

the price of gas in a certain state

changed from

two dollars and 24 cents

to two dollars and 56 cents

calculate the percent of change in the

price of gas

in 2017.

so you need to identify the original

value and the new value

the original value

is 224.

the new value

is 2.56

so now we can calculate the percent

change

it's going to be the new value which is

2.56

minus the original value of 2.24 cents

divided by the original

times 100

now we're going to follow the same

process first

we're going to subtract 2.56

by

2.24 and you should get 0.32

and then

we're going to divide

0.32

by 2.24

and that will give you 0.14

2

9 if you decide to round it

then multiply that by 100

and so this is going to be a percent

increase

and it's point i mean it's

two nine 14.29

so that's the percent change or percent

increase

in the price of gas

in 2017 in that state

number two

john has 2500 in his savings account

he adds 400 to it in january

calculate the percent change in the

value of his savings account in january

so feel free to take a minute and work

on that problem

so we need to identify the new value

and the original value

so what is the original value in this

problem

the original value is the money that he

has in its savings account it's 2500.

now what is the new value

in his savings account

it's not 400 remember he adds 400 to it

the new value is going to be 2500

plus 400

or basically 2900

the 400 is basically the change in the

account in january

so now let's calculate the percent

change

it's the new value

of 2900

minus the original value of 2500

divided by the original value

times 100 percent

so twenty nine hundred minus twenty five

hundred

that's four hundred

and let's divide four hundred by twenty

five hundred

400 divided by 2500 is point sixteen

and if you multiply point sixteen by a

hundred percent

you'll get sixteen percent

so this is a percent increase

so his savings account went up by 16

during that month

here's another one

the population of cats on island x was

1500

next month

the population grew by 250.

what is the percent change in the

population of cats during that month

so first we need to identify the

original value

so what is the original value in this

problem and also what is the new value

the original value is the 1500 cats on a

population

now the population grew by 250 so the

new value is 1500

plus

250.

which gives us a new value of 1750.

so we need to use these two numbers

in the formula

so now let's calculate the percent

change

it's going to be the new value of 1750

minus the original value of 1500 which

will equate to 250

and then divided by the original value

so 1750 minus 1500 that is the change

that's the 250 that we had at the

beginning

and if we divide that by 1500

that

is going to give us

let's see

0.16 repeating i'm going to round it to

0.167

so this will give us a percent increase

of

16.7

percent

and so that's the answer for this

problem

number four

500 students registered for a college

chemistry course

after the first test 140 students

dropped out of the class

what is the percent change

so in this problem identify the new

value

and the original value

the original value you can clearly see

that it's 500 students

the new value

is

the original value

minus the change

140 students dropped out of the class so

that means that there's only 360

of the 500 original students remaining

so now we can calculate the percent

change

so the percent change is the new value

which is 360

minus the original value of 500

divided by

the original value times 100 percent

so 360 minus 500 that's 140 but you need

to use a negative 140 because

the number of students in the class

decreased

so negative 140 divided by 500

let's find the decimal value of

that fraction

you should get negative 0.28

and then multiplying it by 100

we can see that this is a percent

decrease because the answer is negative

so it's negative 28

so that is the percent change in this

chemistry course

you