Mark Up And Markdown Problems With Exercise

Key Concepts

• Percent mark-up and percent markdown.
• Find the percent mark-up.
• Find the selling price.
• Find markdown and sales tax.

3.5 Solve mark-up and markdown problems 

What is mark-up? 

Mark-up is the amount of increase from the cost of an item to its selling price 

What is percent mark-up? 

Mark-up is the amount of increase from the cost of an item to its selling price. The mark-up as a percent increase from the original cost is the percent mark-up. 

The percent mark-up can be determined using the percent equation. 

What is markdown? 

Markdown is the decrease from the original price of an item to its sales price 

What is percent markdown? 

Markdown is the decrease from the original price of an item to its sales price. The markdown as a percent decrease of the original price is the percent markdown. 

Example 1: Luther buys cell phone cases and then decorates them to resell online at a higher price. What is the percent mark-up if he buys each case at $7.20 and sells them at $11.25 after decorating? 

Solution:  

Step 1: 

Draw a bar diagram to represent the problem and to find the mark-up. 

The change in cost is $4.05.  

Step 2: Use the percent equation to find the percent mark-up. 

We know that, part = percent × whole  

Here we understand that, part = change in the cost of the case,  

whole = original cost and p = percent mark-up. 

Let us take percent as p, which we are about to find. 

Change in the cost of the case = percent mark-up × original cost. 

8 = p × 32 

Divide the equation by 7.20 on both sides. 

P =4.05 = p × 7.20 

P = 0.5625 

Express the decimal as a percent by multiplying by 100. 

P = 56.25% 

Therefore, the percent mark-up of the case is 56.25% 

3.5.1 Find the percent mark-up 

Example 1: An item costs $20 before tax and $28 after the sales tax. What is the sales tax rate? 

Solution:  

Step 1: 

Draw a bar diagram to represent the problem and to find the mark-up. 

The change in tax is $8.  

Step 2: Use the percent equation to find the percent mark-up. 

We know that, part = percent × whole  

Here we understand that, part = change in cost, whole = original cost and p = percent mark-up. 

Let us take percent as p, which we are about to find. 

Change in cost = percent mark-up × original cost. 

8 = p × 20 

Divide the equation by 20 on both sides. 

P = 0.20 

Express the decimal as a percent by multiplying by 100. 

P = 20% 

Therefore, the percent mark-up of the item is 20% 

Example 2: The local furniture store pays $110 for a chest of drawers and sells it for $180. Find the percent mark-up on the chest of drawers. 

Solution:  

Step 1: 

Draw a bar diagram to represent the problem and to find the mark-up. 

The change in cost is $40.  

Step 2: Use the percent equation to find the percent mark-up. 

We know that, part = percent × whole  

Here we understand that, part = change in cost, whole = original cost and p = percent mark-up. 

Let us take percent as p, which we are about to find. 

Change in cost of the case = percent mark-up × original cost. 

40 = p × 110 

Divide the equation by 110 on both sides. 

P = 0.3636 

Express the decimal as a percent by multiplying by 100. 

P = 36.36% 

Therefore, the percent mark-up of the furniture is 36.36% 

3.5.2 Find the selling price 

Example 1: A shopkeeper sells a refrigerator for $400 with a profit of 20%. Find the price at which the customer has purchased it. 

Solution: 

Step 1: 

Draw a bar diagram to represent the problem. 

Step 2: Use the percent equation to find the mark-up and the selling price. 

We know that, part = percent × whole  

Here we understand that, part = mark-up, whole = cost price and p = percent mark-up. 

Let us take mark-up as p, which we are about to find. 

Mark-up = percent mark-up × cost price. 

p = 20% × 400 

p = 0.20 × 400 

P = 80 

The mark-up is noticed to be $80. 

The selling price of refrigerator = cost price + mark-up 

        = 400+80 

        = $480. 

Therefore, the selling price of the refrigerator is $480. 

Example 2: Martin sold his flat with a 38% mark-up. If he bought his house for $100,000 two years ago, then find the selling price. 

Solution: 

Step 1: 

Draw a bar diagram to represent the problem. 

Step 2: Use the percent equation to find the mark-up and the selling price. 

We know that, part = percent × whole  

Here we understand that, part = mark-up, whole = cost price and p = percent mark-up. 

Let us take mark-up as p, which we are about to find. 

Mark-up = percent mark-up × cost price. 

p = 38% × 100000 

p = 0.38 × 100000 

P = 38000 

The mark-up is noticed to be $38000. 

The selling price of house  = cost price + mark-up 

= 100000+38000 

= $138000. 

Therefore, the selling price of the house is $138000. 

3.5.3 Find markdown and sales tax 

Example 1: Find the percent markdown for an $80 jacket that is on sale for $48.  

Solution: 

Step 1: 

Draw a bar diagram to represent the problem. 

Step 2: Use the percent equation to find the percent mark-down. 

We know that, part = percent × whole  

Here we understand that, part = change in cost, whole = original cost and p = percent mark-down. 

Let us take percent as p, which we are about to find. 

Change in cost = percent mark-down × original cost. 

32 = p × 80 

Divide the equation by 80 on both sides. 

P = 0.4 

Express the decimal as a percent by multiplying by 100. 

P = 40% 

Therefore, the percent mark-down of the jacket is 40% 

Example 2: Sasha went shopping and decided to purchase a set of bracelets for 30% off the marked price of $50. If she buys the bracelets today, she will be charged a minimum of 3.4% sales tax against the regular 8%. Find her cost price. 

Solution: 

Step 1: Use the percent equation to find the mark-down price of the bracelet. 

We know that, part = percent × whole  

Here we understand that, part = mark-down, whole = original cost and p = percent mark-down. 

Let us take mark-down as p, which we are about to find. 

Mark-down = percent mark-down × original cost. 

p = 30% × 50 

p = 0.30 × 50 

p = 15 

The sale price is $50-$15 = $35. 

Step 2: Use the percent equation to find the sales tax 

We know that, part = percent × whole  

Here we understand that, part = sales tax, whole = sale price and p = percent. 

Let us take sales tax as s, which we are about to find. 

Sales tax = percent × sale price. 

s = 3.4% × 35 

s = 0.034× 35 

s = 0.51 

Exercise:

1. On Saturday, 300 people attended the church. The very next day, it was found that 500 people attended the church. Find the percent mark-up in the attendance?
2. A cycle was bought for $1225 and sold at a gain of $275. Find the percent mark-up?
3. A dealer sells spare parts of the car at a profit margin of 15%. If the sells the wheel of a car for $200, what is the purchase price of the dealer?
4. The price of gas increased by 25% from the last week. What is the price today, if the price at last week was $208 per gallon?          
5. Ruby sells her watch to Jessy at 10% gain. If Ruby bought that watch for $350, find the cost price of Jessy.
6. A hotel sells burgers for $25. If a 2.4% is tax levied, what is the selling price?
7. A customer bargains and purchases an item for $40. If it is priced at $75 find the percent mark-down.
8. Find the sales price of a $4200 article with a 32% mark-down.
9. A $400 suit is marked down by 24%. Find the sale price rounded to the nearest dollar?
10. A department store buys 450 shirts for $2700 and sells them for $10 each. Find the percent mark-up.

What have we learned?

• Percent mark-up and percent markdown.
• Finding percent mark-up.
• Finding the selling price.
• Finding mark-down and sales tax.