Monetary Percentage - PSAT Math
Card 1 of 294
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?
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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?
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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?
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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?
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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?
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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?
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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?
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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?
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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?
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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?
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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)?
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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?
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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?
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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?
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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?
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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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Sale price: 
off: 
coupon: 
Sale price:
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Company 
is introducing its newest smartphone model, so it is reducing the price of the previous model by 85%. If the previous model used to sell for $180, what is its new price?
Company
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The sale price is 85% less than the original which is the same as 15% of the original 
. 
The sale price is 85% less than the original which is the same as 15% of the original
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An item is full-priced at $75. It is reduced by 10%, and then you apply a 25% off coupon to that price. There is a 7% sales tax on your purchase. How much do you pay?
An item is full-priced at $75. It is reduced by 10%, and then you apply a 25% off coupon to that price. There is a 7% sales tax on your purchase. How much do you pay?
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The item begins at $75. it is 10% off.
You then take an additional 25% off:
There is then a 7% sales tax:
The item begins at $75. it is 10% off.
You then take an additional 25% off:
There is then a 7% sales tax:
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A shirt at the store has a retail price of $17.50. If a customer buys the shirt and uses a 15% coupon, how much does he pay for the shirt, assuming there is no sales tax?
(Round to two decimal places.)
A shirt at the store has a retail price of $17.50. If a customer buys the shirt and uses a 15% coupon, how much does he pay for the shirt, assuming there is no sales tax?
(Round to two decimal places.)
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If a customer has a 15% coupon, the customer will pay 85% of the original price. To solve this problem, simply multiply the original price of the shirt by the percent of the price the customer still has to pay:
Round to the nearest two decimal places, and we see that the price of the shirt is $14.88.
If a customer has a 15% coupon, the customer will pay 85% of the original price. To solve this problem, simply multiply the original price of the shirt by the percent of the price the customer still has to pay:
Round to the nearest two decimal places, and we see that the price of the shirt is $14.88.
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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?
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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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