7th Grade Common Core Math Worksheets - Free Printable

Problem Set: Discount, Markup, Markdown, and Tax Problems

Below is a detailed solution for each problem in the provided image. Each step is explained clearly to ensure understanding.

---

#### Problem 1:
In Tulsa, Oklahoma, the sales tax is 7.9%. If you buy an $850 television in Tulsa, how much tax will you pay?

- Step 1: Identify the sales tax rate and the cost of the television.
- Sales tax rate = 7.9% = 0.079
- Cost of television = $850

- Step 2: Calculate the tax amount.
\[
\text{Tax} = \text{Cost of television} \times \text{Sales tax rate}
\]
\[
\text{Tax} = 850 \times 0.079 = 67.15
\]

- Answer: The tax you will pay is $67.15.

---

#### Problem 2:
A sweater costs $35. Find the total cost of the sweater if the sales tax is 5%.

- Step 1: Identify the sales tax rate and the cost of the sweater.
- Sales tax rate = 5% = 0.05
- Cost of sweater = $35

- Step 2: Calculate the tax amount.
\[
\text{Tax} = \text{Cost of sweater} \times \text{Sales tax rate}
\]
\[
\text{Tax} = 35 \times 0.05 = 1.75
\]

- Step 3: Calculate the total cost.
\[
\text{Total cost} = \text{Cost of sweater} + \text{Tax}
\]
\[
\text{Total cost} = 35 + 1.75 = 36.75
\]

- Answer: The total cost of the sweater is $36.75.

---

#### Problem 3:
Estimate which of the following would be a 15% tip for a bill of $38.49.
- [A] $5.80
- [B] $3.85
- [C] $1.90
- [D] $7.70

- Step 1: Approximate the bill to simplify calculations.
- Bill ≈ $38.50

- Step 2: Calculate 15% of the bill.
\[
\text{Tip} = \text{Bill} \times 0.15
\]
\[
\text{Tip} = 38.50 \times 0.15 = 5.775 \approx 5.80
\]

- Answer: The closest estimate is [A] $5.80.

---

#### Problem 4:
What is the salesperson’s commission on a $1300 sale if the commission rate is 10%?

- Step 1: Identify the commission rate and the sale amount.
- Commission rate = 10% = 0.10
- Sale amount = $1300

- Step 2: Calculate the commission.
\[
\text{Commission} = \text{Sale amount} \times \text{Commission rate}
\]
\[
\text{Commission} = 1300 \times 0.10 = 130
\]

- Answer: The salesperson’s commission is $130.

---

#### Problem 5:
At the end of the summer, lawn furniture selling at a market price of $482 is on sale for 20% off. What is the discount?

- Step 1: Identify the discount rate and the original price.
- Discount rate = 20% = 0.20
- Original price = $482

- Step 2: Calculate the discount amount.
\[
\text{Discount} = \text{Original price} \times \text{Discount rate}
\]
\[
\text{Discount} = 482 \times 0.20 = 96.40
\]

- Answer: The discount is $96.40.

---

#### Problem 6:
A bookstore offers a 15% discount to its employees. Suppose an employee has a coupon worth $5 off any item and wants to buy a book that costs $45. What is the final cost of the book if the employee discount is taken first and then the coupon is subtracted?

- Step 1: Calculate the discount on the book.
- Discount rate = 15% = 0.15
- Original price = $45
\[
\text{Discount} = 45 \times 0.15 = 6.75
\]

- Step 2: Subtract the discount from the original price.
\[
\text{Price after discount} = 45 - 6.75 = 38.25
\]

- Step 3: Subtract the coupon value from the discounted price.
- Coupon value = $5
\[
\text{Final price} = 38.25 - 5 = 33.25
\]

- Answer: The final cost of the book is $33.25.

---

#### Problem 7:
The Book Barn is having a sale. All hardback books are 20% off, and all paperbacks are 10% off. Suppose you buy four paperbacks that originally cost $9 each and two hardbacks that originally cost $20 each. What percent of the total have you saved? Round to the nearest percent.

- Step 1: Calculate the original total cost.
- Cost of one paperback = $9
- Cost of one hardback = $20
- Number of paperbacks = 4
- Number of hardbacks = 2
\[
\text{Original total cost} = (4 \times 9) + (2 \times 20) = 36 + 40 = 76
\]

- Step 2: Calculate the discounted prices.
- Discount on paperbacks = 10% = 0.10
- Discount on hardbacks = 20% = 0.20
\[
\text{Discounted price of one paperback} = 9 \times (1 - 0.10) = 9 \times 0.90 = 8.10
\]
\[
\text{Discounted price of one hardback} = 20 \times (1 - 0.20) = 20 \times 0.80 = 16.00
\]

- Step 3: Calculate the total cost after discounts.
\[
\text{Total cost after discounts} = (4 \times 8.10) + (2 \times 16.00) = 32.40 + 32.00 = 64.40
\]

- Step 4: Calculate the savings.
\[
\text{Savings} = \text{Original total cost} - \text{Total cost after discounts}
\]
\[
\text{Savings} = 76 - 64.40 = 11.60
\]

- Step 5: Calculate the percentage saved.
\[
\text{Percentage saved} = \left( \frac{\text{Savings}}{\text{Original total cost}} \right) \times 100
\]
\[
\text{Percentage saved} = \left( \frac{11.60}{76} \right) \times 100 \approx 15.26\%
\]

- Answer: The percent of the total saved is 15% (rounded to the nearest percent).

---

#### Problem 8:
A department store purchases a coat for $95. To sell the coat to customers, the price is increased by 27%. What is the new price of the coat?

- Step 1: Identify the purchase price and the markup rate.
- Purchase price = $95
- Markup rate = 27% = 0.27

- Step 2: Calculate the markup amount.
\[
\text{Markup} = \text{Purchase price} \times \text{Markup rate}
\]
\[
\text{Markup} = 95 \times 0.27 = 25.65
\]

- Step 3: Calculate the new price.
\[
\text{New price} = \text{Purchase price} + \text{Markup}
\]
\[
\text{New price} = 95 + 25.65 = 120.65
\]

- Answer: The new price of the coat is $120.65.

---

#### Problem 9:
The regular price of a dress is $80. The price has been marked up by 23%. What is the amount of markup?

- Step 1: Identify the regular price and the markup rate.
- Regular price = $80
- Markup rate = 23% = 0.23

- Step 2: Calculate the markup amount.
\[
\text{Markup} = \text{Regular price} \times \text{Markup rate}
\]
\[
\text{Markup} = 80 \times 0.23 = 18.40
\]

- Answer: The amount of markup is $18.40.

---

#### Problem 10:
The owner of a music store received a shipment of stereos at a cost of $160.00 each. What will the selling price be if he applies a 45% markup?

- Step 1: Identify the cost price and the markup rate.
- Cost price = $160.00
- Markup rate = 45% = 0.45

- Step 2: Calculate the markup amount.
\[
\text{Markup} = \text{Cost price} \times \text{Markup rate}
\]
\[
\text{Markup} = 160 \times 0.45 = 72.00
\]

- Step 3: Calculate the selling price.
\[
\text{Selling price} = \text{Cost price} + \text{Markup}
\]
\[
\text{Selling price} = 160 + 72 = 232.00
\]

- Answer: The selling price is $232.00.

---

Final Answers:

1. $67.15
2. $36.75
3. [A] $5.80
4. $130
5. $96.40
6. $33.25
7. 15%
8. $120.65
9. $18.40
10. $232.00

Boxed Final Answer:
\[
\boxed{67.15, 36.75, A, 130, 96.40, 33.25, 15, 120.65, 18.40, 232.00}
\]