Finding Original Price Given Sale Price and Percent Discount ... - Free Printable

To solve the problems in the worksheet, we need to find the original price of an item given the sale price and the discount percentage. The general formula to find the original price is:

\[
\text{Original Price} = \frac{\text{Sale Price}}{1 - \text{Discount Rate}}
\]

Where the discount rate is expressed as a decimal.

Let's solve each problem step by step.

---

Problem 1:

If Peter pays \$84 to buy a watch after a discount of 20%, find the original price of the watch.

- Sale Price = \$84
- Discount Rate = 20% = 0.20

Using the formula:
\[
\text{Original Price} = \frac{\$84}{1 - 0.20} = \frac{\$84}{0.80} = 105
\]

Answer: The original price of the watch is \$105.

---

Problem 2:

The price of a math book after a discount of 25% is \$36. What is the original price of the math book?

- Sale Price = \$36
- Discount Rate = 25% = 0.25

Using the formula:
\[
\text{Original Price} = \frac{\$36}{1 - 0.25} = \frac{\$36}{0.75} = 48
\]

Answer: The original price of the math book is \$48.

---

Problem 3:

If you buy 3 shirts, you get a 10% discount. If you paid \$270 for 6 shirts, what is the original price of a T-shirt?

- Sale Price for 6 shirts = \$270
- Discount Rate = 10% = 0.10

First, find the original price for 6 shirts:
\[
\text{Original Price for 6 shirts} = \frac{\$270}{1 - 0.10} = \frac{\$270}{0.90} = 300
\]

Since this is the price for 6 shirts, the original price of one shirt is:
\[
\text{Original Price per shirt} = \frac{\$300}{6} = 50
\]

Answer: The original price of a T-shirt is \$50.

---

Problem 4:

The price of a desktop computer after discount was \$1,600. If the discount was 20%, what was the original price?

- Sale Price = \$1,600
- Discount Rate = 20% = 0.20

Using the formula:
\[
\text{Original Price} = \frac{\$1,600}{1 - 0.20} = \frac{\$1,600}{0.80} = 2,000
\]

Answer: The original price of the desktop computer is \$2,000.

---

Problem 5:

Find the original price of a motorbike if you got a 10% discount and paid a final price of \$2,160 for it.

- Sale Price = \$2,160
- Discount Rate = 10% = 0.10

Using the formula:
\[
\text{Original Price} = \frac{\$2,160}{1 - 0.10} = \frac{\$2,160}{0.90} = 2,400
\]

Answer: The original price of the motorbike is \$2,400.

---

Problem 6:

What is the original price of an apple if you got a 20% discount and paid \$1 for it?

- Sale Price = \$1
- Discount Rate = 20% = 0.20

Using the formula:
\[
\text{Original Price} = \frac{\$1}{1 - 0.20} = \frac{\$1}{0.80} = 1.25
\]

Answer: The original price of the apple is \$1.25.

---

Problem 7:

Mike bought an item for \$14,000 after a discount of 30%. What was the original price of the item Mike bought?

- Sale Price = \$14,000
- Discount Rate = 30% = 0.30

Using the formula:
\[
\text{Original Price} = \frac{\$14,000}{1 - 0.30} = \frac{\$14,000}{0.70} = 20,000
\]

Answer: The original price of the item is \$20,000.

---

Problem 8:

If a Play Station was bought for \$450 after a 10% discount, what was the original price of the Play Station?

- Sale Price = \$450
- Discount Rate = 10% = 0.10

Using the formula:
\[
\text{Original Price} = \frac{\$450}{1 - 0.10} = \frac{\$450}{0.90} = 500
\]

Answer: The original price of the Play Station is \$500.

---

Problem 9:

What is the original price of a TV set if you paid \$1,035 for it after a discount of 10%?

- Sale Price = \$1,035
- Discount Rate = 10% = 0.10

Using the formula:
\[
\text{Original Price} = \frac{\$1,035}{1 - 0.10} = \frac{\$1,035}{0.90} = 1,150
\]

Answer: The original price of the TV set is \$1,150.

---

Problem 10:

If you get a 15% discount and pay \$340 for a telephone, what is its original price?

- Sale Price = \$340
- Discount Rate = 15% = 0.15

Using the formula:
\[
\text{Original Price} = \frac{\$340}{1 - 0.15} = \frac{\$340}{0.85} = 400
\]

Answer: The original price of the telephone is \$400.

---

Final Answers:

1. \$105
2. \$48
3. \$50
4. \$2,000
5. \$2,400
6. \$1.25
7. \$20,000
8. \$500
9. \$1,150
10. \$400

\boxed{105, 48, 50, 2000, 2400, 1.25, 20000, 500, 1150, 400}