### 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:

- 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?
- A cycle was bought for $1225 and sold at a gain of $275. Find the percent mark-up?
- 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?
- 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?
- Ruby sells her watch to Jessy at 10% gain. If Ruby bought that watch for $350, find the cost price of Jessy.
- A hotel sells burgers for $25. If a 2.4% is tax levied, what is the selling price?
- A customer bargains and purchases an item for $40. If it is priced at $75 find the percent mark-down.
- Find the sales price of a $4200 article with a 32% mark-down.
- A $400 suit is marked down by 24%. Find the sale price rounded to the nearest dollar?
- 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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