How to find the sale price - Algebra
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A girl in County A spent $75 before a 7.25% sales tax and a girl in County B spent $70 before an 8% sales tax. How much more money did the girl from County A spend than the girl from County B after sales tax was applied? Round to the nearest hundredth.
A girl in County A spent $75 before a 7.25% sales tax and a girl in County B spent $70 before an 8% sales tax. How much more money did the girl from County A spend than the girl from County B after sales tax was applied? Round to the nearest hundredth.
County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$75 * 0.0725 = $5.4375
Add the original price and the sales tax.
$75 + $5.4375 = $80.4375
County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$70 * 0.08 = $5.6
Add the original price and the sales tax.
$70 + $5.6 = $75.6
Then take the difference.
80.4375 – 75.6 = 4.8375
Round to the nearest hundredth: $4.84
County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$75 * 0.0725 = $5.4375
Add the original price and the sales tax.
$75 + $5.4375 = $80.4375
County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$70 * 0.08 = $5.6
Add the original price and the sales tax.
$70 + $5.6 = $75.6
Then take the difference.
80.4375 – 75.6 = 4.8375
Round to the nearest hundredth: $4.84
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A perfume that an employee of a discount store wants to buy was marked down 40%; the employee gets a 25% discount on merchandise she buys there. The two discounts together add up to what percent discount off the original regular price?
A perfume that an employee of a discount store wants to buy was marked down 40%; the employee gets a 25% discount on merchandise she buys there. The two discounts together add up to what percent discount off the original regular price?
Let us say for the sake of simplicity that the perfume costs $100.00 before discount. Then a 40% discount means that the discount is 40% of $100, or $40, and the new price is $60. Then the employee gets a discount of 25% of the $60, or 
; she will pay 
.
She ends up paying 45% of the original purchase price; that is, she gets a net discount of 55%.
Let us say for the sake of simplicity that the perfume costs $100.00 before discount. Then a 40% discount means that the discount is 40% of $100, or $40, and the new price is $60. Then the employee gets a discount of 25% of the $60, or
She ends up paying 45% of the original purchase price; that is, she gets a net discount of 55%.
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A hat that an employee of a discount store wants to buy was marked down 30%; the employee gets a 15% discount on merchandise she buys there. The two discounts together add up to what percent discount off the original regular price?
A hat that an employee of a discount store wants to buy was marked down 30%; the employee gets a 15% discount on merchandise she buys there. The two discounts together add up to what percent discount off the original regular price?
Let us say for the sake of simplicity that the hat costs $100.00 before discount. Then a 30% discount means that the discount is 30% of $100, or $30, and the new price is $70. Then the employee gets a discount of 15% of the $70, or 
; she will pay 
.
She ends up paying 59.5% of the original purchase price; that is, she gets a net discount of 40.5%.
Let us say for the sake of simplicity that the hat costs $100.00 before discount. Then a 30% discount means that the discount is 30% of $100, or $30, and the new price is $70. Then the employee gets a discount of 15% of the $70, or
She ends up paying 59.5% of the original purchase price; that is, she gets a net discount of 40.5%.
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Mary was shopping for a new dress, and found one she liked for $48. Better yet, it was 25% off. How much did Mary pay for the dress?
Mary was shopping for a new dress, and found one she liked for $48. Better yet, it was 25% off. How much did Mary pay for the dress?
To find the sale price we can set up a proportion. 25/100 = x/48. We keep the 100 and 48 both on the bottom of the fraction since they represent the "whole". x represents the discount off the full price of the dress. To solve this proportion, we cross multiply, yielding 48 * 25 = 100x. Alternatively, if you notice that 25/100 simplifies to 1/4, we can use 1/4 in our proportion instead of 25/100, thus, 1/4 = x/48. Then, cross multiplying, we get 48 = 4x, so x = 12. Then we subtract this discount from the original price yielding 48 – 12 = 36; thus, she paid $36 for the dress.
25% = 25/100
(1) * (48) = (4) * (x)
48 = 4x
(48)/4 = (4x)/4
12 = x
The discount is $12.
$48 – $12 = $36
To find the sale price we can set up a proportion. 25/100 = x/48. We keep the 100 and 48 both on the bottom of the fraction since they represent the "whole". x represents the discount off the full price of the dress. To solve this proportion, we cross multiply, yielding 48 * 25 = 100x. Alternatively, if you notice that 25/100 simplifies to 1/4, we can use 1/4 in our proportion instead of 25/100, thus, 1/4 = x/48. Then, cross multiplying, we get 48 = 4x, so x = 12. Then we subtract this discount from the original price yielding 48 – 12 = 36; thus, she paid $36 for the dress.
25% = 25/100
(1) * (48) = (4) * (x)
48 = 4x
(48)/4 = (4x)/4
12 = x
The discount is $12.
$48 – $12 = $36
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Robin sees that a jacket at the mall has been marked down 20% from an original price of $49.99. Taking into account the sales tax of 8%, which is applied after taking the discount, how much will Robin have left over if she brought $60 to the mall?
Robin sees that a jacket at the mall has been marked down 20% from an original price of $49.99. Taking into account the sales tax of 8%, which is applied after taking the discount, how much will Robin have left over if she brought $60 to the mall?
After the discount, she will pay for the remaining cost of the jacket. This cost will be equal to the percent remaining after the discount.
100% – 20% = 80%
She will pay for 80% of the original cost.
80% = 0.80
Add in the sales tax.
8% = 0.08
Subtract the final price from Robin's budget of $60.
After the discount, she will pay for the remaining cost of the jacket. This cost will be equal to the percent remaining after the discount.
100% – 20% = 80%
She will pay for 80% of the original cost.
80% = 0.80
Add in the sales tax.
8% = 0.08
Subtract the final price from Robin's budget of $60.
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There is a sale for 20% off on a sweater your grandma wants to buy you for christmas. The original price is $15.98. How much does the sweater cost with the discount?
There is a sale for 20% off on a sweater your grandma wants to buy you for christmas. The original price is $15.98. How much does the sweater cost with the discount?
To find the answer, you must first convert the sales percentage to a decimal by moving the decimal left two places.
Then, multiply the total cost by the decimal.
This gives us the amount of the discount. To find the remaining cost, we subtract that number from the original cost to get the answer.
To find the answer, you must first convert the sales percentage to a decimal by moving the decimal left two places.
Then, multiply the total cost by the decimal.
This gives us the amount of the discount. To find the remaining cost, we subtract that number from the original cost to get the answer.
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A shirt that originally cost $45 is on sale. The sale price is 15% off of the original price. What is the sale price?
A shirt that originally cost $45 is on sale. The sale price is 15% off of the original price. What is the sale price?
First, calculate 15% of $45:
Therefore, the discount is $6.75 off of the price of the shirt. To find the sale price, subtract the discount from the original price:
First, calculate 15% of $45:
Therefore, the discount is $6.75 off of the price of the shirt. To find the sale price, subtract the discount from the original price:
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A hat that an employee of a discount store wants to buy was marked down 20%; the employee gets a 10% discount on merchandise she buys there. The two discounts together add up to what percent discount off the original regular price?
A hat that an employee of a discount store wants to buy was marked down 20%; the employee gets a 10% discount on merchandise she buys there. The two discounts together add up to what percent discount off the original regular price?
Let us say for the sake of simplicity that the hat costs $100.00 before discount. Then a 20% discount means that the discount is 20% of $100, or $20, and the new price is $80. Then the employee gets a discount of 10% of the $80, or 
; she will pay 
.
She ends up paying 72% of the original purchase price; that is, she gets a net discount of 28%.
Let us say for the sake of simplicity that the hat costs $100.00 before discount. Then a 20% discount means that the discount is 20% of $100, or $20, and the new price is $80. Then the employee gets a discount of 10% of the $80, or
She ends up paying 72% of the original purchase price; that is, she gets a net discount of 28%.
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An item is marked up by 25% and then marked down by 40%. What percentage of the original price is the new price?
An item is marked up by 25% and then marked down by 40%. What percentage of the original price is the new price?
The quickest way to do this problem is to realize that a "mark up" is done by adding that percentage to 100%. For instance a 40% markup is performed by multiplying by 1.4. A markdown is done by subtracting that percentage from 100%. For instance, a 25% markdown is performed by multiplying by 0.75. (Think of the latter case like this: it is 75% of its original price.)
Based on these remarks, the problem is easy. While we do not know our price we know that the first markup gives us:
To this, we now perform the mark down:
Multiply out your coefficients (the numbers in the front):
This is the same thing as saying "75% of the original price (
)."
The quickest way to do this problem is to realize that a "mark up" is done by adding that percentage to 100%. For instance a 40% markup is performed by multiplying by 1.4. A markdown is done by subtracting that percentage from 100%. For instance, a 25% markdown is performed by multiplying by 0.75. (Think of the latter case like this: it is 75% of its original price.)
Based on these remarks, the problem is easy. While we do not know our price we know that the first markup gives us:
To this, we now perform the mark down:
Multiply out your coefficients (the numbers in the front):
This is the same thing as saying "75% of the original price (
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The price of an item is $18 after a 25% discount. What was its original price?
The price of an item is $18 after a 25% discount. What was its original price?
If something is discounted 
, it is really 
of its original price. The question is thus asking, "
of what is 
?" This can be translated as:
Solve for 
by dividing both sides of the equation by 
:
Therefore, it was originally 
.
If something is discounted
Solve for
Therefore, it was originally
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The price of an item is $25 after a 60% discount. What was the original price?
The price of an item is $25 after a 60% discount. What was the original price?
When an item is marked down 
, it is 
of its original price. The question could be rephrased as "
of what is 
?" This could be rewritten as an equation rather simply:
Solve for x by dividing both sides by 0.40:
.
When an item is marked down
Solve for x by dividing both sides by 0.40:
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At a department store, a high-end pair of jeans normally costs $170. This week, the store is having a sale and marked the jeans 20% off. However, Jane is an employee of the store and gets an additional 25% discount off the already discounted sale price. How much will Jane pay for the jeans?
At a department store, a high-end pair of jeans normally costs $170. This week, the store is having a sale and marked the jeans 20% off. However, Jane is an employee of the store and gets an additional 25% discount off the already discounted sale price. How much will Jane pay for the jeans?
The first step is to find 20% of $170. This can be done easily by multiplying 170 by 0.2, yielding $34. We subtract 34 from 170 to get the initial sale price, $136. Next, we have to take 25% of that already discounted figure, and we do this by multiplying 136 by 0.25. Again, we happen to get $34, and after we subtract that number from 136 we get our final price, $102. The other answer choices are either the result of forgetting a step or of simple calculation errors.
The first step is to find 20% of $170. This can be done easily by multiplying 170 by 0.2, yielding $34. We subtract 34 from 170 to get the initial sale price, $136. Next, we have to take 25% of that already discounted figure, and we do this by multiplying 136 by 0.25. Again, we happen to get $34, and after we subtract that number from 136 we get our final price, $102. The other answer choices are either the result of forgetting a step or of simple calculation errors.
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Mr. Jones is trying to restrict his expenditures on groceries to 12% of his salary. He makes $756.00 weekly, and he lives in a state where the sales tax rate is 6.125% on groceries. Calculate the maximum price before sales tax of the groceries Mr. Jones can buy each week in order to stick to his self-imposed limit.
Mr. Jones is trying to restrict his expenditures on groceries to 12% of his salary. He makes $756.00 weekly, and he lives in a state where the sales tax rate is 6.125% on groceries. Calculate the maximum price before sales tax of the groceries Mr. Jones can buy each week in order to stick to his self-imposed limit.
According to his rule, Mr. Jones can spend 12% of $756.00 weekly.
This is the amount he can spend after sales tax.
Let 
be the price of the groceries before the sales tax is figured in.
The sales tax paid is 6.125% of 
, or 
, so the amount paid for the groceries is 
.
Since Mr. Jones is limited to spending $90.72, this means that 
. We can solve the inequality for 
.
The maximum amount Mr. Jones can spend before tax is $85.48.
According to his rule, Mr. Jones can spend 12% of $756.00 weekly.
This is the amount he can spend after sales tax.
Let
The sales tax paid is 6.125% of
Since Mr. Jones is limited to spending $90.72, this means that
The maximum amount Mr. Jones can spend before tax is $85.48.
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Bob is thinking about buying a truck that usually costs $20,000 because there is a 20% discount on all vehicles this week. How much money would Bob save if he bought the truck when it is on sale?
Bob is thinking about buying a truck that usually costs $20,000 because there is a 20% discount on all vehicles this week. How much money would Bob save if he bought the truck when it is on sale?
This week, there is a 20% discount on the truck, which means that its price will be 20% lower than its usual price of $20,000. If $20,000 is the regular price, then its sale price must be 80% of $20,000, which is $16,000. Thus, Bob would be saving $4,000 by taking advantage of the discount.
This week, there is a 20% discount on the truck, which means that its price will be 20% lower than its usual price of $20,000. If $20,000 is the regular price, then its sale price must be 80% of $20,000, which is $16,000. Thus, Bob would be saving $4,000 by taking advantage of the discount.
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The original price of an item is $20. When the store sells the item, it marks it up by 20%, after which a 6% tax is added. What is the final price of this item?
The original price of an item is $20. When the store sells the item, it marks it up by 20%, after which a 6% tax is added. What is the final price of this item?
There are two ways to do this problem. The easiest way is to realize that we can represent two subsequent increases by saying, "After the markup, it is 120% of the original price and then the post-tax cost is 106% of that price." This can be represented as two consecutive multiplications:
The more difficult way would be first to multiply $20 by 0.20, getting $4. Adding this to $20, we have $24 for the "tag price." Now, you will have to multiply $24 by 0.06 to get the amount of tax, which would be $1.44. Then, adding this to $24, you get $25.44, which you could have gotten much more quickly using the method shown above.
There are two ways to do this problem. The easiest way is to realize that we can represent two subsequent increases by saying, "After the markup, it is 120% of the original price and then the post-tax cost is 106% of that price." This can be represented as two consecutive multiplications:
The more difficult way would be first to multiply $20 by 0.20, getting $4. Adding this to $20, we have $24 for the "tag price." Now, you will have to multiply $24 by 0.06 to get the amount of tax, which would be $1.44. Then, adding this to $24, you get $25.44, which you could have gotten much more quickly using the method shown above.
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A television set that normally costs $1200 is 20% off this week. How much would a customer pay for the discounted television set?
A television set that normally costs $1200 is 20% off this week. How much would a customer pay for the discounted television set?
To find the discount, you must simply find 20% of $1200, the television set's original price.
20% of $1200 is $240
Now subtract that number from 1200
To find the discount, you must simply find 20% of $1200, the television set's original price.
20% of $1200 is $240
Now subtract that number from 1200
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A dealership is having a special event where all cars are given a 15% discount. What is the sale price of a car that normally costs $18,000?
A dealership is having a special event where all cars are given a 15% discount. What is the sale price of a car that normally costs $18,000?
With a 15% discount, the car must be priced at 85% of its original price (100% minus the 15% discount). Since the car is originally priced at $18,000, the sale price must be 85% of $18,000. To find 85% of $18,000 you must convert it to its decimal equivalent (0.85) and multiply it by $18,000: 
to get a solution of 15,300.
With a 15% discount, the car must be priced at 85% of its original price (100% minus the 15% discount). Since the car is originally priced at $18,000, the sale price must be 85% of $18,000. To find 85% of $18,000 you must convert it to its decimal equivalent (0.85) and multiply it by $18,000:
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A television set that normally costs $800 is on sale for 20% off this week. If a customer uses a coupon that takes an additional 10% off the sale price, how much would the customer pay for the television set?
A television set that normally costs $800 is on sale for 20% off this week. If a customer uses a coupon that takes an additional 10% off the sale price, how much would the customer pay for the television set?
The original price of the television set is $800. Taking off 20% of the price, the television set is priced at $640: 
. With the additional 10% off from the coupon, the price becomes $576: 
.
The original price of the television set is $800. Taking off 20% of the price, the television set is priced at $640:
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You find a computer you like and discover that its sale price is $650, which is 70% of its original price. What is the original price of that computer?
You find a computer you like and discover that its sale price is $650, which is 70% of its original price. What is the original price of that computer?
The sale price of something is determined by the following formula
Where 
represents the sale price, 
is the percentage of the original price (in decimal form), and 
represents the original price.
In this problem, we are given that the sale price of the computer is $650 , which is 70% of the original price. In decimal form, this percentage is written as 0.70. We are to find the original price. Plug in the values
Solve for 
by dividing both sides by 0.70
So the original price of the computer is $928.57.
The sale price of something is determined by the following formula
Where
In this problem, we are given that the sale price of the computer is $650 , which is 70% of the original price. In decimal form, this percentage is written as 0.70. We are to find the original price. Plug in the values
Solve for
So the original price of the computer is $928.57.
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At a clothing store, winter coats are on sale at a discount of 20%. You found a coat you like and looked at the price tag saying that the regular price is $250. Find the coat's sale price.
At a clothing store, winter coats are on sale at a discount of 20%. You found a coat you like and looked at the price tag saying that the regular price is $250. Find the coat's sale price.
With a 20% discount, the sale price of the coat will be 80% (100%-20%=80%) of the original price. The sale price of something is normally calculated as
Where 
is the sale price, 
is the percent of the original price, and 
is the original price. Given that the original price of the coat is $250 and knowing that the sale price is at 80% (or 0.80) of the original price, the sale price is calculated as
So the sale price of the coat is $200.
With a 20% discount, the sale price of the coat will be 80% (100%-20%=80%) of the original price. The sale price of something is normally calculated as
Where
So the sale price of the coat is $200.
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