Percentage - SAT Math
Card 0 of 1440
The cost of a hat increases by 15% and then decreases by 35%. After the two price changes, the new price of the hat is what percent of the original?
The cost of a hat increases by 15% and then decreases by 35%. After the two price changes, the new price of the hat is what percent of the original?
The easiest way to do percentage changes is to keep them all in one equation. Therefore, we would say that an increase of 15% is the same as multiplying the original value by 1.15. Likewise, we would say that a discount by 35% is the same as multiplying the original by .65.
For our problem, let the hat cost X dollars originally. Therefore, after its increase, it costs 1.15_X_ dollars. Now, we can consider this new price as the whole to which the discount will be applied. Therefore, a 35% reduction is (1.15_X_) * 0.65.
Simplifying, we get 0.7475, or 74.75%.
The easiest way to do percentage changes is to keep them all in one equation. Therefore, we would say that an increase of 15% is the same as multiplying the original value by 1.15. Likewise, we would say that a discount by 35% is the same as multiplying the original by .65.
For our problem, let the hat cost X dollars originally. Therefore, after its increase, it costs 1.15_X_ dollars. Now, we can consider this new price as the whole to which the discount will be applied. Therefore, a 35% reduction is (1.15_X_) * 0.65.
Simplifying, we get 0.7475, or 74.75%.
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If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
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If the price of a TV was decreased from $3,000 to $1,800, by what percent was the price decreased?
If the price of a TV was decreased from $3,000 to $1,800, by what percent was the price decreased?
The price was lowered by $1,200 which is 40% of $3,000.
The price was lowered by $1,200 which is 40% of $3,000.
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The cost of a shirt in January is 
dollars. In February, the cost is decreased by 10%. In March, the cost is decreased by another 10%. By what percentage did the shirt decrease in total between January and March?
The cost of a shirt in January is
The best way to answer this question is to plug in a number for n. Since you are working with percentages, it may be easiest to use 100 for n.
We know that in the month of February, the cost of this shirt was decreased by 10%. Because 10% of 100 is $10, the new cost of the shirt is $90.
In March, the cost of the shirt decreased another 10%. 10% of 90 is 9, so the cost of the shirt is now $81.
To find the total percentage decrease, you must divide 81 by 100 and subtract it from 1.
1 – (81/100) = 1 – 0.81 = 0.19
The total decrease was 19%.
The best way to answer this question is to plug in a number for n. Since you are working with percentages, it may be easiest to use 100 for n.
We know that in the month of February, the cost of this shirt was decreased by 10%. Because 10% of 100 is $10, the new cost of the shirt is $90.
In March, the cost of the shirt decreased another 10%. 10% of 90 is 9, so the cost of the shirt is now $81.
To find the total percentage decrease, you must divide 81 by 100 and subtract it from 1.
1 – (81/100) = 1 – 0.81 = 0.19
The total decrease was 19%.
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At a certain store, prices for all items were assigned in January. Each month after that, the price was 20% less than the price the previous month. If the price of an item was x dollars in January, approximately what was the price in dollars of the item in June?
At a certain store, prices for all items were assigned in January. Each month after that, the price was 20% less than the price the previous month. If the price of an item was x dollars in January, approximately what was the price in dollars of the item in June?
The question tells us that the price in January was x. To find the price in February, we decrease the price of x by 20%, which is the same as taking 80% of x. (In general, a P% decrease of a number is the same as (100 – P)% times that number). Continue to take 0.8 times the previous month's price to find the next month's price until we have the price for June, as follows:
January Price: x
February Price: 0.8 * January Price = 0.8_x_
March Price: 0.8 * February Price = 0.8 * 0.8_x_ = 0.82 * x
April Price: 0.8 * March Price = 0.8 * 0.8 * 0.8_x_ = 0.83 * x
May Price: 0.8 * April Price = 0.8 * 0.8 * 0.8 * 0.8_x_ = 0.84 * x
June Price: 0.8 * May Price = 0.8 * 0.8 * 0.8 * 0.8 * 0.8_x_ = 0.85 * x; therefore, the price in June was 0.85 ≈ 0.328 ≈ 0.33 times the original price.
The question tells us that the price in January was x. To find the price in February, we decrease the price of x by 20%, which is the same as taking 80% of x. (In general, a P% decrease of a number is the same as (100 – P)% times that number). Continue to take 0.8 times the previous month's price to find the next month's price until we have the price for June, as follows:
January Price: x
February Price: 0.8 * January Price = 0.8_x_
March Price: 0.8 * February Price = 0.8 * 0.8_x_ = 0.82 * x
April Price: 0.8 * March Price = 0.8 * 0.8 * 0.8_x_ = 0.83 * x
May Price: 0.8 * April Price = 0.8 * 0.8 * 0.8 * 0.8_x_ = 0.84 * x
June Price: 0.8 * May Price = 0.8 * 0.8 * 0.8 * 0.8 * 0.8_x_ = 0.85 * x; therefore, the price in June was 0.85 ≈ 0.328 ≈ 0.33 times the original price.
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The sale of a tablet decreased from $500 to $450. By what percentage did the cost decrease?
The sale of a tablet decreased from $500 to $450. By what percentage did the cost decrease?
Set up the following ratio
50/500 = n/100
The cost of the tablet decreased by $50. The original cost is $500; therefore, 50 is the numerator and 500 is the denominator on the left side of the ratio.
Since a percentage is a part of a whole, n symbolizes the the percentage decrease.
To solve for n, you can cross multiply. So, 50(100) = n(500).
n = 10%
Set up the following ratio
50/500 = n/100
The cost of the tablet decreased by $50. The original cost is $500; therefore, 50 is the numerator and 500 is the denominator on the left side of the ratio.
Since a percentage is a part of a whole, n symbolizes the the percentage decrease.
To solve for n, you can cross multiply. So, 50(100) = n(500).
n = 10%
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On Monday, the price of a shirt costs x dollars. On Tuesday, the manager puts the shirt on sale for 10% off Monday's price. On Wednesday, the manager increases the price of the shirt by 10% of Tuesday's price. Describe the change in price from Monday to Wednesday.
On Monday, the price of a shirt costs x dollars. On Tuesday, the manager puts the shirt on sale for 10% off Monday's price. On Wednesday, the manager increases the price of the shirt by 10% of Tuesday's price. Describe the change in price from Monday to Wednesday.
To find the cost on Tuesday, take 10% off Monday's price. In other words, find 90% of Monday's price. This is simply 0.9_x_. If we are to now add 10% of this value back onto itself to find Wednesday's price, we want 100% + 10%, or 110% of 0.9_x_.
1.1(0.9_x_) = 0.99_x_
This value is 1% smaller than x.
To find the cost on Tuesday, take 10% off Monday's price. In other words, find 90% of Monday's price. This is simply 0.9_x_. If we are to now add 10% of this value back onto itself to find Wednesday's price, we want 100% + 10%, or 110% of 0.9_x_.
1.1(0.9_x_) = 0.99_x_
This value is 1% smaller than x.
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If a rectangle's length decreases by fifteen percent, and its width decreases by twenty percent, then by what percent does the rectangle's area decrease?
If a rectangle's length decreases by fifteen percent, and its width decreases by twenty percent, then by what percent does the rectangle's area decrease?
Let's call the original length and width of the rectangle 
and 
, respectively.
The initial area, 
, of the rectangle is equal to the product of the length and the width. We can represent this with the following equation:
Next, let 
and 
represent the length and width, respectively, after they have been decreased. The final area will be equal to 
, which will be equal to the product of the final length and width.
We are asked to find the change in the area, which essentially means we want to compare 
and 
. In order to do this, we will need to find an expression for 
in terms of 
and 
. We can rewrite 
and 
in terms of 
and 
.
First, we are told that the length is decreased by fifteen percent. We can think of the full length as 100% of the length. If we take away fifteen percent, we are left with 100 – 15, or 85% of the length. In other words, the final length is 85% of the original length. We can represent 85% as a decimal by moving the decimal two places to the left.
= 85% of 
= 
Similarly, if we decrease the width by 20%, we are only left with 80% of the width.
= 80% of 
= 
We can now express the final area in terms of 
and 
by substituting the expressions we just found for the final length and width.
= (
)(
) = 
Lastly, let's apply the formula for percent of change, which will equal the change in the area divided by the original area. The change in the area is equal to the final area minus the original area.
percent change = 
(100%)
=
(100%)
=
(100%) = –0.32(100%) = –32%
The negative sign indicates that the rectangle's area decreased. The change in the area was a decrease of 32%.
The answer is 32.
Let's call the original length and width of the rectangle
The initial area,
Next, let
We are asked to find the change in the area, which essentially means we want to compare
First, we are told that the length is decreased by fifteen percent. We can think of the full length as 100% of the length. If we take away fifteen percent, we are left with 100 – 15, or 85% of the length. In other words, the final length is 85% of the original length. We can represent 85% as a decimal by moving the decimal two places to the left.
Similarly, if we decrease the width by 20%, we are only left with 80% of the width.
We can now express the final area in terms of
Lastly, let's apply the formula for percent of change, which will equal the change in the area divided by the original area. The change in the area is equal to the final area minus the original area.
percent change =
=
=
The negative sign indicates that the rectangle's area decreased. The change in the area was a decrease of 32%.
The answer is 32.
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The cost of a load of laundry is reduced by 
. The cost is then reduced 2 weeks later by another 
. What is the overall reduction?
The cost of a load of laundry is reduced by
The original reduction brings the total to 
of the original value. Taking a 
discount off that price gives 
of the original value. This means the reduction had been 
.
The original reduction brings the total to
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A dress is reduced in price by 
, but it still doesn't sell, so the manager discounts it by another 
. What is the total percentage discount?
A dress is reduced in price by
For these type of questions, it is always best to pretend that we are beginning with a $100 item and to calculate from there.
If an item that is $100 is discounted by 35%, and then another 10%, the new price is 58.5%.
The price difference (discount) is $41.5 for every $100, or:
The total discount is 41.5%.
For these type of questions, it is always best to pretend that we are beginning with a $100 item and to calculate from there.
If an item that is $100 is discounted by 35%, and then another 10%, the new price is 58.5%.
The price difference (discount) is $41.5 for every $100, or:
The total discount is 41.5%.
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In his most recent film, it was estimated that Joaquin Phoenix was paid 
of the 
budget. In his next roll, he is expected to make 
less. How much money should Joaquin expect to make for his next film?
In his most recent film, it was estimated that Joaquin Phoenix was paid
First, we find how much Mr. Phoenix made in his most recent movie
Then, we decrease this by fifteen percent according the to the formula:
First, we find how much Mr. Phoenix made in his most recent movie
Then, we decrease this by fifteen percent according the to the formula:
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If there is a 10% sale on an item, and then 9% sales tax is applied to that after-sale price, then what is the total cost of the item including tax as a percentage of its pre-sale sticker price?
If there is a 10% sale on an item, and then 9% sales tax is applied to that after-sale price, then what is the total cost of the item including tax as a percentage of its pre-sale sticker price?
A 10% sale means that the post-sale price of the item is now 90%, or 0.9 of the original cost of the item. We then apply 9% sales tax by multiplying the 0.9 by 109%, or 1.09. 0.9 * 1.09 = .981, so the total cost of the item is 98.1% of the original pre-sale sticker price.
For percentage problems that do not deal with a specific starting number, it is always helpful to plug in 100 for the starting number. Here, we would then have a post-sale price of 90 dollars, and if we calculate the sales tax for the 90-dollar item it would be 90 * 0.09 = $8.10. THis gives us a total cost of 90 + 8.10 = $98.10, or 98.1% of the original 100-dollar price.
A 10% sale means that the post-sale price of the item is now 90%, or 0.9 of the original cost of the item. We then apply 9% sales tax by multiplying the 0.9 by 109%, or 1.09. 0.9 * 1.09 = .981, so the total cost of the item is 98.1% of the original pre-sale sticker price.
For percentage problems that do not deal with a specific starting number, it is always helpful to plug in 100 for the starting number. Here, we would then have a post-sale price of 90 dollars, and if we calculate the sales tax for the 90-dollar item it would be 90 * 0.09 = $8.10. THis gives us a total cost of 90 + 8.10 = $98.10, or 98.1% of the original 100-dollar price.
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A certain state charges sales tax at a rate of 8.75% per dollar spent. John spends $127.50 total, including tax, on clothes. What was the total price of the clothing before tax was added?
A certain state charges sales tax at a rate of 8.75% per dollar spent. John spends $127.50 total, including tax, on clothes. What was the total price of the clothing before tax was added?
Since we know the total price with tax, we simply need to work backwards to remove the tax from the total price and find the price of the clothing itself. This can be done as follows:
Clothing Price or C = Total price / 1 + tax rate
C = $127.50/(1 + 0.0875) = $117.24
Since we know the total price with tax, we simply need to work backwards to remove the tax from the total price and find the price of the clothing itself. This can be done as follows:
Clothing Price or C = Total price / 1 + tax rate
C = $127.50/(1 + 0.0875) = $117.24
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Lisa just bought a desktop computer. The computer cost $1500, the keyboard cost $100, and the mouse cost $25. If the local sales tax is 7%, what was the total cost of her purchases?
Lisa just bought a desktop computer. The computer cost $1500, the keyboard cost $100, and the mouse cost $25. If the local sales tax is 7%, what was the total cost of her purchases?
Total Tax = 
=
Total Cost = Computer + Keyboard + Mouse + Tax = 
Total Tax =
Total Cost = Computer + Keyboard + Mouse + Tax =
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Harry, on his first lunch date with Sally, decides to put the entire bill on his credit card. If the bill came to $28 and Harry wants to leave an 18% tip, what is the total amount that he should pay?
Harry, on his first lunch date with Sally, decides to put the entire bill on his credit card. If the bill came to $28 and Harry wants to leave an 18% tip, what is the total amount that he should pay?
To find an 18% increase, multiply by 1.18.
To find an 18% increase, multiply by 1.18.
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Mike spent $30 on food and $50 on non-food products in the supermarket. There's a sales tax of 10% on non-food products only. How much did Mike spend in total at the supermarket?
Mike spent $30 on food and $50 on non-food products in the supermarket. There's a sales tax of 10% on non-food products only. How much did Mike spend in total at the supermarket?
Since sales tax is only applicable to non-food products only, we can multiply 50 by 1.1 to get the total price of non-food products. In this case, it is $55. Add this value to the $30 spent on food for a total of $85.
Since sales tax is only applicable to non-food products only, we can multiply 50 by 1.1 to get the total price of non-food products. In this case, it is $55. Add this value to the $30 spent on food for a total of $85.
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Cynthia buys 2 shirts, each costing $35, a pair of pants for $40 and a belt for $18. At the register the total she owes is $138.24. What is the rate of sales tax in her state?
Cynthia buys 2 shirts, each costing $35, a pair of pants for $40 and a belt for $18. At the register the total she owes is $138.24. What is the rate of sales tax in her state?
To find the amount of sales tax, take the difference in the total before and after tax 
and divide by the price before tax. This gives 0.08 or 8%.
To find the amount of sales tax, take the difference in the total before and after tax
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Jack is at the grocery store. He buys 
in groceries, and groceries are not taxed in his state. He also buys 
in other items, which are taxed at 
(not yet applied). How much is his total?
Jack is at the grocery store. He buys
Jack's groceries are not taxed, so they cost 
, but his other items are taxed. We will calculate the price with the tax:
We will add the two together
Jack's groceries are not taxed, so they cost
We will add the two together
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A dealership is selling a used car with a sticker price of 
. If state sales tax is 
, how much will the taxes on purchasing the car be?
A dealership is selling a used car with a sticker price of
The amount paid in sales tax is determined by multiplying the decimal value of the tax rate by the sticker price of the car:
The amount paid in sales tax is determined by multiplying the decimal value of the tax rate by the sticker price of the car:
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Jenny buys a blouse that is priced at $45. She pays a total of $48.15, what is the rate of tax on the blouse?
Jenny buys a blouse that is priced at $45. She pays a total of $48.15, what is the rate of tax on the blouse?
The purpose of this question is to calculate tax rates using dollar amounts.
First, the amount of tax payed must be determined. This is done by finding the difference between the amount paid and the listed price
,
which equals $3.15.
Then, that must be translated into a percentage of $45.
Therefore,
, yielding .07 of 1. This is a 7% tax rate.
The purpose of this question is to calculate tax rates using dollar amounts.
First, the amount of tax payed must be determined. This is done by finding the difference between the amount paid and the listed price
which equals $3.15.
Then, that must be translated into a percentage of $45.
Therefore,
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