Percentage - PSAT Math
Card 0 of 700
Write 7.5% as a fraction.
Write 7.5% as a fraction.
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
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Write as a fraction: 22%
Write as a fraction: 22%
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
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25% of 64 is equal to 5% of what number?
25% of 64 is equal to 5% of what number?
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
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When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?
When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?
The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.
If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.
Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.
Now, we set these two expressions equal to one another.
(9/10)y = (3/20)x
Multiply both sides by 20 to eliminate fractions.
18_y_ = 3_x_
The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.
18_y_ = 3_x_
Divide both sides by 3.
6_y_ = x
Divide both sides by y.
6 = x/y
Thus, the ratio of x to y is 6.
The answer is 6.
The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.
If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.
Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.
Now, we set these two expressions equal to one another.
(9/10)y = (3/20)x
Multiply both sides by 20 to eliminate fractions.
18_y_ = 3_x_
The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.
18_y_ = 3_x_
Divide both sides by 3.
6_y_ = x
Divide both sides by y.
6 = x/y
Thus, the ratio of x to y is 6.
The answer is 6.
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Convert 62% into simplified fraction form.
Convert 62% into simplified fraction form.
To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:
To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:
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Your friend works at a computer store. She can get a 15% discount on any item’s current price for as many items as she wants. She wants to buy a laptop for \$2200 and a smartphone for \$200. Local sales tax where your friend lives is 8%. What will be her total cost to buy these two items?
Your friend works at a computer store. She can get a 15% discount on any item’s current price for as many items as she wants. She wants to buy a laptop for \$2200 and a smartphone for \$200. Local sales tax where your friend lives is 8%. What will be her total cost to buy these two items?
First, find the total price of the products $2200 + $200 = \$2400.
Then apply the 15% discount: \$2400 * 0.15 = \$360
Subtract the discount: \$2400 – $360 = $2040.
Then find cost of sales tax $2040 * 0.08 = 163.20
Add: $2040 + 163.20 = \$2203.20.
(An alternative would be to multiply the cost by 1.08.)
First, find the total price of the products $2200 + $200 = \$2400.
Then apply the 15% discount: \$2400 * 0.15 = \$360
Subtract the discount: \$2400 – $360 = $2040.
Then find cost of sales tax $2040 * 0.08 = 163.20
Add: $2040 + 163.20 = \$2203.20.
(An alternative would be to multiply the cost by 1.08.)
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If Stacy paid \$26 for a shirt at a 30%-off sale, what was the original price of the shirt?
If Stacy paid \$26 for a shirt at a 30%-off sale, what was the original price of the shirt?
If the shirt is \$26 after 30% was taken off, then cost of the the shirt (\$26) is 70% of the original price.
We set up an equation that states:
0.7_x_ = 26 (0.7 is the decimal value of 70%)
x = 26/0.7 = \$37.14
If the shirt is \$26 after 30% was taken off, then cost of the the shirt (\$26) is 70% of the original price.
We set up an equation that states:
0.7_x_ = 26 (0.7 is the decimal value of 70%)
x = 26/0.7 = \$37.14
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Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was \$207.27, what was the original price (before all discounts) of the camera?
Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was \$207.27, what was the original price (before all discounts) of the camera?
To reconstruct an original price from a sale price, use:
Original Price – Original Price * Mark-down-percent = Sale Price, or
Original Price * (1 - Mark-down-percent) = Sale Price
To do a double mark-down problem, we must do this twice. For the 10%:
Original Sale Price * (1 – 10%) = \$207.27
Original Sale Price = \$207.27/0.9 = \$230.30.
For the pre-all-discount price,
Original Price * (1 – 30%) = \$230.30
Original Price = $230.30/0.7 = $329.00.
To reconstruct an original price from a sale price, use:
Original Price – Original Price * Mark-down-percent = Sale Price, or
Original Price * (1 - Mark-down-percent) = Sale Price
To do a double mark-down problem, we must do this twice. For the 10%:
Original Sale Price * (1 – 10%) = \$207.27
Original Sale Price = \$207.27/0.9 = \$230.30.
For the pre-all-discount price,
Original Price * (1 – 30%) = \$230.30
Original Price = $230.30/0.7 = $329.00.
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An mp3 player costs \$100 on day one. On day two, the shop owner decides to decrease the price by 10% of the day one price. However, on day three the owner changes her mind and raises the price by 10% of the day two price. What is the new price of the mp3 player?
An mp3 player costs \$100 on day one. On day two, the shop owner decides to decrease the price by 10% of the day one price. However, on day three the owner changes her mind and raises the price by 10% of the day two price. What is the new price of the mp3 player?
10% of the day one price = 0.1(100) = \$10.
Therefore the day two price = 100 - 10 = \$90.
10% of the day two price = 0.1(90) = \$9.
Therefore the day three price = 90 + 9 = \$99.
10% of the day one price = 0.1(100) = \$10.
Therefore the day two price = 100 - 10 = \$90.
10% of the day two price = 0.1(90) = \$9.
Therefore the day three price = 90 + 9 = \$99.
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A pair of shoes originally sells for \$250. There is a sale, and the shoes are then sold for 20% off. The shoes are then marked down an additional 35%. If sales tax is 7%, what can you buy the pair of shoes for today, including tax?
A pair of shoes originally sells for \$250. There is a sale, and the shoes are then sold for 20% off. The shoes are then marked down an additional 35%. If sales tax is 7%, what can you buy the pair of shoes for today, including tax?
The shoes are first marked down 20%.
20% of $250 = .2 x $250 = \$50
Sales price = \$250 - $50 = $200
The second markdown is 35%.
35% of $200 = .35 x $200 = \$70
New price = \$200 - $70 = $130
Calculate the sales tax:
7% of $130 = .07 x $130 = \$9.10
Total price = \$130 + $9.10 = $139.10
The shoes are first marked down 20%.
20% of $250 = .2 x $250 = \$50
Sales price = \$250 - $50 = $200
The second markdown is 35%.
35% of $200 = .35 x $200 = \$70
New price = \$200 - $70 = $130
Calculate the sales tax:
7% of $130 = .07 x $130 = \$9.10
Total price = \$130 + $9.10 = $139.10
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The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
Let us assume that the original purse is \$100. The price after the first reduction is \$80. After the second reduction the price is now \$56. The difference between 100 and 56 is 44, giving 44% off.
Let us assume that the original purse is \$100. The price after the first reduction is \$80. After the second reduction the price is now \$56. The difference between 100 and 56 is 44, giving 44% off.
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Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally \$50, how much did she pay?
Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally \$50, how much did she pay?
The original price was \$50. First you take 30% off (50 * (100 - 30)/100 = \$35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
The original price was \$50. First you take 30% off (50 * (100 - 30)/100 = \$35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
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A store is having a sale. If you buy one widget for the regular price of \$20, you can buy a second widget for 40% off the regular price. How much per widget does a customer save by buying two widgets during the sale instead of buying two widgets at the regular price?
A store is having a sale. If you buy one widget for the regular price of \$20, you can buy a second widget for 40% off the regular price. How much per widget does a customer save by buying two widgets during the sale instead of buying two widgets at the regular price?
Widget 1 costs \$20.
Widget 2 is on sale for 40%(\$20) off, or \$8 off, or \$20 – $8 = $12.
Two widgets during the sale cost $20 + $12 = \$32.
Two widgets at regular price cost \$20 + $20 = $40.
The total amount saved during the sale is \$40 – \$32 = \$8.
This is the savings for two widgets, so the savings for one widget is \$8/2 = \$4.
Widget 1 costs \$20.
Widget 2 is on sale for 40%(\$20) off, or \$8 off, or \$20 – $8 = $12.
Two widgets during the sale cost $20 + $12 = \$32.
Two widgets at regular price cost \$20 + $20 = $40.
The total amount saved during the sale is \$40 – \$32 = \$8.
This is the savings for two widgets, so the savings for one widget is \$8/2 = \$4.
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A \$225 dress goes on sale for 75% off. It is then discounted again for 10% off. How much money was saved on by the final purchase?
A \$225 dress goes on sale for 75% off. It is then discounted again for 10% off. How much money was saved on by the final purchase?
The answer is \$174.37.
The dress originally cost \$225 but when it went on sale for 75% off we multiply the sale cost by 0.75. We see that through the sale we save \$168.75 makeing the new cost of the dress \$56.25.
Now we take the new cost of the dress (\$56.25) and multiply that by 0.10 to represent the 10% discount. From this we see we save an additional \$5.63 making the final cost of the dress \$50.63.
The total savings on the dress sum up to \$174.37.
The answer is \$174.37.
The dress originally cost \$225 but when it went on sale for 75% off we multiply the sale cost by 0.75. We see that through the sale we save \$168.75 makeing the new cost of the dress \$56.25.
Now we take the new cost of the dress (\$56.25) and multiply that by 0.10 to represent the 10% discount. From this we see we save an additional \$5.63 making the final cost of the dress \$50.63.
The total savings on the dress sum up to \$174.37.
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A stove is regularly priced for \$300. What is the difference one would pay when buying it at a 20% discount rather than a 10% discount, with an additional 10% discount off the sale price?
A stove is regularly priced for \$300. What is the difference one would pay when buying it at a 20% discount rather than a 10% discount, with an additional 10% discount off the sale price?
Buying the stove at a 20% discount would be \$240. If one buys it at a sale of 10%, with another 10% off then the price would be \$243, so the difference is \$3
20% of 300 is 0.2 * 300 = 60 → 300 – 60 = 240
10% of 300 is 0.1 * 300 = 30 → 300 – 30 = 270
10% of 270 is 0.1 * 270 = 27 → 270 – 27 = 243
243 – 240 = 3
Buying the stove at a 20% discount would be \$240. If one buys it at a sale of 10%, with another 10% off then the price would be \$243, so the difference is \$3
20% of 300 is 0.2 * 300 = 60 → 300 – 60 = 240
10% of 300 is 0.1 * 300 = 30 → 300 – 30 = 270
10% of 270 is 0.1 * 270 = 27 → 270 – 27 = 243
243 – 240 = 3
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Mark sells his car to Mike for 95% of the amount he originally paid. Mike then discounts the car 20% and sells it to Max. Max paid \$300. How much did Mark buy his car for (rounded to the nearest dollar)?
Mark sells his car to Mike for 95% of the amount he originally paid. Mike then discounts the car 20% and sells it to Max. Max paid \$300. How much did Mark buy his car for (rounded to the nearest dollar)?
Apply your percentage knowledge. Starting value times percentage equals end value. $300/(1 – 0.2) = $375. $375/0.95 = $395.
Apply your percentage knowledge. Starting value times percentage equals end value. $300/(1 – 0.2) = $375. $375/0.95 = $395.
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The costs for Lizzie’s party are as follows: \$6000 to cater, \$1200 for the DJ, \$2000 for decorating, and \$2200 for the venue rental. Lizze can choose to apply a discount of 10% for the caterer and decorating but is then charged an additional 30% for the DJ and venue. What is the minimum price she will pay?
The costs for Lizzie’s party are as follows: \$6000 to cater, \$1200 for the DJ, \$2000 for decorating, and \$2200 for the venue rental. Lizze can choose to apply a discount of 10% for the caterer and decorating but is then charged an additional 30% for the DJ and venue. What is the minimum price she will pay?
The discounts are not worth the extra cost. The answer is \$11,400.
The discounts are not worth the extra cost. The answer is \$11,400.
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Mr. Glatfelter trains hunting dogs for a price of \$4000 per dog. If it costs him \$15,000 per month to keep his business open and each dog costs \$1000 to train, how many dogs per month must he train to make a profit?
Mr. Glatfelter trains hunting dogs for a price of \$4000 per dog. If it costs him \$15,000 per month to keep his business open and each dog costs \$1000 to train, how many dogs per month must he train to make a profit?
The answer is 6. 6 hunting dogs gives him a net profit of \$3000. If you picked 5, that’s where Glatfelter breaks even (he doesn’t make a profit or a loss).
The answer is 6. 6 hunting dogs gives him a net profit of \$3000. If you picked 5, that’s where Glatfelter breaks even (he doesn’t make a profit or a loss).
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A dress was originally priced at \$70. In January, it was put on sale for 20% off. Then in February, the sale price was lowered an additional \$10 off of January's price. How much is the dress currently being sold for?
A dress was originally priced at \$70. In January, it was put on sale for 20% off. Then in February, the sale price was lowered an additional \$10 off of January's price. How much is the dress currently being sold for?
The dress started at \$70. In January, it was marked down 20%. \$70 * 0.2 = \$14, so it was being sold for \$70 – $14 = $56. Then we're told its price is again lowered, this time by \$10. Now the price is \$56 – $10 = $46.
The dress started at \$70. In January, it was marked down 20%. \$70 * 0.2 = \$14, so it was being sold for \$70 – $14 = $56. Then we're told its price is again lowered, this time by \$10. Now the price is \$56 – $10 = $46.
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Molly needs to buy a new microwave. Two stores, A and B, sell the exact model microwave that Molly needs to buy; however, stores A and B are selling this microwave at two different prices. Store A is selling the microwave for its regular price of \$250. Store B is having a 20% off sale on all kitchen appliances. If the regular price of the microwave at store B is \$275, how much money will Molly save if she purchases the microwave at store B with the additional 20% discount compared to if she were to purchase the microwave at store A?
Molly needs to buy a new microwave. Two stores, A and B, sell the exact model microwave that Molly needs to buy; however, stores A and B are selling this microwave at two different prices. Store A is selling the microwave for its regular price of \$250. Store B is having a 20% off sale on all kitchen appliances. If the regular price of the microwave at store B is \$275, how much money will Molly save if she purchases the microwave at store B with the additional 20% discount compared to if she were to purchase the microwave at store A?
If Molly buys the microwave at store B at the discounted price, we need to calculate what the price of the microwave is after the 20% discount. In order to do so, we must multiply 20% with the \$275 regular price of the microwave at store B.
20% is 0.20.
So,
0.20 * \$275 = \$55
This is the discount we will receive. That means that we must subtract \$55 from the regular price of \$275.
\$275 – $55 = $220
This is the price of the microwave at store B after the 20% discount.
Now we must compare the prices from store A and B.
Store A sells the microwave for \$250.
Therefore, \$250 – $220 = $30 saved.
If Molly buys the microwave at store B at the discounted price, we need to calculate what the price of the microwave is after the 20% discount. In order to do so, we must multiply 20% with the \$275 regular price of the microwave at store B.
20% is 0.20.
So,
0.20 * \$275 = \$55
This is the discount we will receive. That means that we must subtract \$55 from the regular price of \$275.
\$275 – $55 = $220
This is the price of the microwave at store B after the 20% discount.
Now we must compare the prices from store A and B.
Store A sells the microwave for \$250.
Therefore, \$250 – $220 = $30 saved.
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