# PSAT Math : How to find the sale price

## Example Questions

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### Example Question #1 : How To Find The Sale Price

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? Possible Answers:$329.00

$767.67$82.91

$518.18$290.18

$329.00 Explanation: 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. ### Example Question #1 : How To Find The Sale Price 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?

$98$101

$102$100

$99 Correct answer:$99

Explanation:

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.

### Example Question #1 : How To Find The Sale Price

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?

40%

50%

56%

48%

44%

44%

Explanation:

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. ### Example Question #1 : How To Find The Sale 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?

32

20

4

12

8

4

Explanation:

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. ### Example Question #1 : How To Find The Sale Price 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?

174.37

191.25

16.88

33.75

50.63

174.37

Explanation:

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.

### Example Question #1 : How To Find 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? Possible Answers:$3

$30$5

$20 Correct answer:$3

Explanation:

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 ### Example Question #2 : How To Find The Sale Price 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)?

280

355

395

265

335

395

Explanation:

Apply your percentage knowledge. Starting value times percentage equals end value. $300/(1 – 0.2) =$375. $375/0.95 =$395.

### Example Question #8 : How To Find The Sale Price

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?

$11,000$11,400

$12,160$10,800

$12,440 Correct answer:$11,400

Explanation:

9

7

8

5

6

6

Explanation:

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). ### Example Question #1 : How To Find The Sale Price 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? Possible Answers:$46

$34$52

$60$50

$46 Explanation: 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. 