Finding the Original Price Given the Sale Price and Percent Discount | Math with Mr. J
Summary
TLDRIn 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
📚 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.
📈 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.
Mindmap
Keywords
💡Original Price
💡Sale Price
💡Discount
💡Percent
💡Decimal
💡Variable
💡Equation
💡Isolate the Variable
💡Division
💡Calculation
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
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