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# Mark Up And Markdown Problems With Exercise

Sep 16, 2022

### Key Concepts

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

## 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.

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