Finding the Original Price Given the Sale Price and Percent Discount | Math with Mr. J

Summary

In the 'Math with Mr. J' video, the host teaches viewers how to calculate the original price of an item given its sale price and the discount percentage. Using two examples, he demonstrates the method of setting up an equation where the original price times (100 minus the discount percent) equals the sale price. He explains converting percentages to decimals and solving for the original price through division. The first example finds an original price of $85 for an item sold at $59.50 with a 30% discount. The second example calculates an original price of $249.80 for an item sold at $112.41 with a 55% discount. The video is educational, providing a clear step-by-step approach to solving such problems.

Takeaways

• 🧮 The video explains how to calculate the original price given the sale price and the discount percentage.
• 🔢 The formula used is: Original Price × (100% - Discount %) = Sale Price.
• ✏️ In Example 1, the sale price is $59.50 with a 30% discount, so the equation becomes: Original Price × 70% = 59.50.
• ➗ 100% - 30% equals 70%, which represents the percentage of the original price being paid after the discount.
• 💡 To simplify the equation, convert the percentage to a decimal (70% = 0.70).
• ✂️ After isolating the variable for the original price, the final step is dividing the sale price by the percentage in decimal form: $59.50 ÷ 0.70 = $85.
• 💲 In Example 2, the sale price is $112.41 with a 55% discount, so the equation becomes: Original Price × 45% = 112.41.
• 🔄 100% - 55% equals 45%, so you pay 45% of the original price in this example.
• 🧑‍🏫 Convert 45% to a decimal (0.45) and divide the sale price by this decimal: $112.41 ÷ 0.45 = $249.80.
• 🎯 The video walks through step-by-step examples to help viewers understand how to reverse the discount to find the original price.

Q & A

What is the purpose of the video?

The purpose of the video is to teach viewers how to calculate the original price of an item given its sale price and the discount percentage.

What is the first example's sale price in the video?

The first example's sale price is $59.50.

What discount percentage is used in the first example?

The discount percentage used in the first example is 30%.

How does the video represent the original price mathematically?

The video represents the original price with the variable 'p' and sets up an equation using the formula: original price * (100 - discount percent) = sale price.

What does the conversion of 70 percent to a decimal involve?

The conversion of 70 percent to a decimal involves moving the decimal point two places to the left, resulting in 0.70.

What is the equation used to find the original price in the first example?

The equation used to find the original price in the first example is p * 0.70 = $59.50.

How is the original price isolated in the equation?

The original price is isolated by dividing both sides of the equation by 0.70.

What is the calculated original price for the first example?

The calculated original price for the first example is $85.

What is the sale price in the second example discussed in the video?

The sale price in the second example is $112.41.

What discount percentage is used in the second example?

The discount percentage used in the second example is 55%.

How is the original price calculated in the second example?

The original price in the second example is calculated by dividing the sale price of $112.41 by 0.45 (the decimal equivalent of 45%).

What is the final original price found in the second example?

The final original price found in the second example is $249.80.

Outlines

00:00

📚 Calculating Original Price with a 30% Discount

The first paragraph introduces a method for calculating the original price of an item given its sale price and the discount percentage. The example provided involves a sale price of $59.50 with a 30% discount. The instructor uses the formula: original price times (100 minus discount percent) equals the sale price. The variable 'p' is assigned to the original price, and the equation is set up as p * (100 - 30) = 59.50. The discount percent is converted to a decimal (70% becomes 0.70), and the equation is solved by dividing the sale price by 0.70, resulting in an original price of $85.

05:02

📈 Determining Original Price with a 55% Discount

The second paragraph continues with another example, this time with a sale price of $112.41 and a 55% discount. The process is similar to the first, using the formula to set up the equation as original price times (100 - 55) = $112.41. The discount percent is converted to a decimal (45% becomes 0.45), and the equation is solved by dividing the sale price by 0.45, yielding an original price of $249.80. The paragraph concludes with a summary of the method and a sign-off from the instructor.

Keywords

💡Original Price

The 'Original Price' refers to the initial cost of an item before any discounts or sales are applied. In the video, the main theme revolves around calculating this original price given the sale price and the discount percentage. It's a fundamental concept in retail and consumer economics, as it helps customers understand the true value of an item and the savings they are receiving from a discount. For example, the script uses the term when setting up equations to find the original price of an item that was sold at a 30% discount.

💡Sale Price

The 'Sale Price' is the amount for which an item is sold after discounts or promotions have been applied. It is a key term in the video as it represents the known quantity used to solve for the unknown original price. The script mentions a sale price of 'fifty-nine dollars and fifty cents' as part of the first example, highlighting how to use this information to calculate the original price.

💡Discount

A 'Discount' is a reduction in the original price of an item, often as a promotional strategy or special offer. The video script discusses how to calculate the original price when the sale price and the discount percentage are known. The term is crucial as it directly impacts the consumer's decision-making process and the perceived value of a purchase. The script provides a discount example of 'thirty percent' to demonstrate the calculation process.

💡Percent

In the context of the video, 'Percent' is used to express the discount rate applied to the original price. It is a way to quantify the portion of the original price that is not paid due to the discount. The script explains converting the discount percent to a decimal for mathematical calculations, which is essential for solving the equation to find the original price.

💡Decimal

A 'Decimal' is a part of a number that represents a fraction of ten, hundred, thousand, etc. In the video, the term is used when converting percentages to decimals for calculation purposes. The script demonstrates the conversion by moving the decimal point two places to the left, which is a common method for translating percentages into a form usable in equations.

💡Variable

A 'Variable' is a symbol, often a letter, that represents an unknown quantity in a mathematical expression or equation. In the script, 'p' is used as a variable to represent the unknown original price. The video explains how to isolate the variable through mathematical operations to solve for the original price, which is a fundamental concept in algebra.

💡Equation

An 'Equation' is a statement that asserts the equality of two expressions. In the video, equations are set up to represent the relationship between the original price, the discount, and the sale price. The script uses equations to guide viewers through the process of calculating the original price, illustrating the mathematical logic behind the calculations.

💡Isolate the Variable

To 'Isolate the Variable' means to manipulate an equation so that the variable of interest is alone on one side of the equation. This is a common technique in algebra used to solve for the variable. The video script demonstrates this by dividing both sides of the equation by a certain number to isolate 'p' and find the original price.

💡Division

In the video, 'Division' is the mathematical operation used to isolate the variable in an equation. It is the process of splitting a number into equal parts. The script shows how division is used to divide the sale price by the decimal equivalent of the discount percentage to find the original price, which is a key step in the calculation.

💡Calculation

A 'Calculation' is the process of computing or estimating a value or quantity. The video focuses on calculations related to discounts and sale prices. The script provides step-by-step calculations for determining the original price from the sale price and discount percentage, which is essential for understanding the mathematical concepts being taught.

Highlights

Introduction to calculating the original price given the sale price and discount.

Use of an equation to represent the relationship between original price, discount, and sale price.

Explanation of using the formula: original price * (100 - discount percent) = sale price.

Example 1: Calculation with a sale price of $59.50 and a 30% discount.

Conversion of the discount percent to a decimal for calculation purposes.

Isolating the variable 'p' representing the original price by dividing by the decimal.

Result of Example 1: The original price is $85.

Example 2: Calculation with a sale price of $112.41 and a 55% discount.

Conversion of 55% to a decimal to find the sale price as a percentage of the original price.

Isolating the variable 'p' by dividing the sale price by the decimal equivalent of the discount.

Result of Example 2: The original price is $249.80.

Emphasis on the importance of keeping the equation balanced by performing the same operation on both sides.

Explanation of how subtracting the discount percent from 100% gives the percentage paid.

Practical application of the method in real-world scenarios such as retail pricing.

Encouragement for viewers to apply this method to calculate original prices in various situations.

Conclusion and thanks for watching, with a sign-off until the next video.

Transcripts

[Music]

welcome to math with mr j

[Music]

in this video i'm going to cover how to

calculate the original price of

something given the sale price and what

the discount was let's jump into our

examples starting with number one where

we have a sale price of fifty nine

dollars and fifty cents and a discount

of thirty percent so we need to find

what the original price of that item was

before the discount was taken off we can

do this by setting up an equation now i

do want to mention that there are

different ways to go about these types

of problems but i'm going to use the

original price

times 100

minus the discount percent equals the

sale price so let's set this up for

number one now we don't know the

original price so we are going to use a

variable p to represent the original

price and then plug in everything else

we are given so we have p

that represents the original price

times 100

minus the discount percent of 30 percent

well that's going to give us

70 percent

equals

59.50

now where did i get that 70

again that's 100

minus the discount we're given

right here 30

so 100

minus 30

equals 70 percent now let's talk about

what that one hundred percent minus the

discount percent means this will give us

what percent of the original price we

are paying one hundred percent

represents the full original price and

we subtract the discount percent to see

what percent of the original price we

are paying so for number one again we

did 100

minus 30

and that gives us

70

we are paying 70 of the original price

now let's convert that percent to a

decimal so we can move forward within

our equation here and remember percent

to decimal move the decimal twice to the

left so the decimal comes at the end of

70 end of a whole number here and we

need to move it once

twice to the left so again we're

converting that percent to a decimal so

let's move on here and rewrite our

equation with the percent in decimal

form so we have the original price which

is a variable of p because it's an

unknown

times

70 as a decimal is 70 hundredths

and that equals our sale price of 59.50

so we have a one-step equation here we

need to isolate our variable here so we

have p times 70 hundredths what's the

opposite of multiplication well division

so we need to divide that side by 70

hundredths and that's going to cancel

out our 70 hundredths and isolate our

variable

now whatever we do to one side we have

to do to the other in order to keep our

equation balanced

so let's divide this side by 70

hundredths as well

so our variable of p the original price

is now isolated and we can do 59.50

divided by 70 hundredths to get our

original price and that's going to give

us

85

so 85

is

our original price

let's move on to number two and do

another example so we have a sale price

of

and 41 112.41

and a discount of 55 percent let's find

out what the original price was so we'll

set up our equation so we have the

original price

times

well 100 percent minus 55

gives us

45 percent so we are paying 45 percent

of the original price and that gives us

our sale price of

dollars

and 41 cents

let's convert our percent to a decimal

by moving the decimal twice to the left

remember a decimal comes at the end of a

whole number so once

twice

and we get 45 hundredths so let's

rewrite this in decimal form

so 45 hundredths

and that gives us our sale price

we will rewrite that

and now we have a one-step equation so

let's divide both sides by 45 hundredths

in order to isolate our original price

that variable p

so divide by 45 hundredths

and remember whatever you do to one side

you have to do to the other so divide by

45 hundredths

and that gives us our original price so

p is now isolated and we have 112

dollars and 41 cents divided by 45

hundredths and that gives us

249

and 80

cents

so our original price

249 dollars

and 80 cents

so there you have it there's how you

calculate the original price given the

sale price and the discount i hope that

helped

thanks so much for watching

until next time

peace