Percent Increase and Decrease Word Problems
Summary
TLDRThis 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
📈 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.
💼 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.
📉 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.
Mindmap
Keywords
💡Percent of Change
💡Formula
💡New Value
💡Original Value
💡Increase
💡Decrease
💡Positive Percent Change
💡Negative Percent Change
💡Word Problems
💡Calculation
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
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