**Calculating Markups and Markdowns :**

A markup is one kind of percent increase. We can use a bar model to represent the retail price of an item, that is, the total price including the markup.

An example of a percent decrease is a discount, or markdown. A price after a markdown may be called a sale price. We can also use a bar model to represent the price of an item including the markdown.

**Mark up ----> Increasing **

To get profit in a business, a trader increases the cost price and sells the product. This increment in price is called as "Mark up"

This "Mark up can either be in percent or in dollars.

**Mark Down ----> Decreasing**

To increase the sale, stores will decrease the price of a product by giving offer or discount. This offer or discount is called as "Mark down".

This mark down can either be in percent or in dollars.

To do mark up and mark down word problems answers, let us go through the hints related to "Markup and Mark down"

**Hint 1 :**

**Cost price and marked up percentage are given.**

**Cost price = C.P, Marked up percentage = M %**

**Then, Selling price (S.P) = (100+M)% x C.P**

**Hint 2 :**

**List price and marked down percentage are given.**

**List price = L.P, Marked down percentage = M %**

**Then, Selling price (S.P) = (100 - M)% x L.P**

**Hint 3 :**

**List price price and marked down value (in dollars ) are given. **

**List price = L.P, Marked down value = $M**

**Then, mark down rate = ( M / L.P ) x 100 %**

**Hint 4 :**

**Cost price and marked up value are given**

**Cost price = C.P, Marked up value = $M**

**Then, mark up rate = ( M / C.P ) x 100 % **

**Hint 5 :**

**Cost price and selling price are given. **

**Cost price = C.P, Selling price = S.P and S.P > C.P**

**So, Gain = S.P - C.P **

**Then, mark up rate = ( Gain / C.P ) x 100 %**

**Example 1 : **

To make a profit, stores mark up the prices on the items they sell. A sports store buys skateboards from a supplier for s dollars. What is the retail price for skateboards that the manager buys for $35 and $56 after a 42% markup ?

**Solution : **

**Step 1 : **

Use a bar model.

Draw a bar for the cost of the skateboard S.

Then draw a bar that shows the markup: 42% of S, or 0.42S.

These bars together represent the cost plus the markup.

That is

S + 0.42S

**Step 2 :**

Retail price = Original cost + Markup

= S + 0.42S

= 1S + 0.42S

= 1.42S

**Step 3 : **

Use the expression to find the retail price of each skateboard.

S = $35 ----> Retail price = 1.42($35) = $49.70

S = $56 ----> Retail price = 1.42($56) = $79.52

Let us look at the next example on "Calculating markups and markdowns".

**Example 2 : **

A discount store marks down all of its holiday merchandise by 20% off the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23.

**Solution : **

**Step 1 : **

Use a bar model.

Draw a bar for the regular price P.

Then draw a bar that shows the discount: 20% of P, or 0.2P.

The difference between these two bars represents the price minus the discount.

That is,

P - 0.2P

**Step 2 :**

Sale price = Original price - Markdown

= p - 0.2p

= 1p - 0.2p

= 0.8p

**Step 3 :**

Use the expression to find the sale price of each decoration.

p = $16 ---> Sale price = 0.8($16) = $12.80

p = $23 ---> Sale price = 0.8($23) = $18.40

Let us look at the next example on "Calculating markups and markdowns".

**Example 3 : **

A computer store used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.

**Solution : **

Selling price (S.P) = (100+M)% x C.P

Here, M = 40, C.P = $25

Then, S.P = (100 + 40)% x 25

S.P = 140% x 25

S.P = 1.4 x 25 = $35

Hence, the selling price is $35.

Let us look at the next example on "Calculating markups and markdowns".

**Example 4 : **

A golf store pays its wholesaler $40 for a certain club, and then sells it to a golfer for $75. What is the markup rate?

**Solution : **

Cost price (C.P) = $ 40

Selling price (S.P) = $ 75

Mark up value = 75 - 40 = $ 35

Mark up rate = (35/40)x100 % = 87.5 %

Hence, the mark up rate is 87.5 %

Let us look at the next example on "Calculating markups and markdowns".

**Example 5 : **

A store uses a 40% markup on cost. Find the cost of a pair of shoes that sells for $63.

**Solution : **

Selling price (S.P) = (100+M)% x C.P ---------(1)

Here, S.P = $ 63, M = 40

Plugging the above values in (1)

(1)-----------> 63 = (100+40)% x C.P

63 = 140% x C.P ---------> 63 = 1.4 x C.P

63/1.4 = C.P ---------> 45 = C.P

Hence, the cost of a pair of shoes is $ 45.

Let us look at the next example on "Calculating markups and markdowns".

**Example 6 :**

A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the mark up rate.

**Solution :**

Let the cost price be $100.

Then, marked price (M.P) = $120

Let the selling price be "X"

From the above picture, we get

90% of (M.P) = X

(0.9).120 = X

108 = X --------> S.P = 108

Cost price = $100, Selling Price = $108 ------> Mark up rate = 8 %

Hence, the mark up rate is 8%.

Let us look at the next example on "Calculating markups and markdowns".

**Example 7 :**

A person wants to get 20% mark up rate after selling his object at 20% discount. Find the required percentage increase in marked price.

**Solution :**

Let the cost price be $100.

Then, the selling price = $120

Let the marked price be "X"

From the above picture, we get

80% of (M.P) = S.P

(0.8)X = 120

X = 150 --------> M.P = 150

Cost price = $100, Marked Price = $150

Hence, the required percentage increase = 50%.

Let us look at the next example on "Calculating markups and markdowns".

**Example 8 : **

A product that regularly sells for $425 is marked down to $318.75. What is the discount rate?

**Solution : **

Regular price = $ 425

Marked down price = $ 318.75

Marked down value = 425 - 318.75 = 106.25

Marked down rate = (106.25 / 425) x 100 %

Marked down rate = 25 %

Hence, the marked down rate is 25 %

Let us look at the next example on "Calculating markups and markdowns".

**Example 9 : **

A product is marked down 15%; the sale price is $127.46. What was the original price?

**Solution : **

Selling price (S.P) = (100 - M)% x Original price ---------(1)

Here, S.P = 127.46, M = 15

Plugging the above values in (1), we get

127.46 = (100 - 15) x Original price

127.46 = 85% x Original price

127.46 = 0.85 x Original price

127.46 / 0.85 = Original price

149.95 = Original price

Hence, the original price is $ 149.95.

Let us look at the next example on "Calculating markups and markdowns".

**Example 10 : **

A product is originally priced at $55 is marked 25% off. What is the sale price?

**Solution : **

Selling price (S.P) = (100 - M)% x L.P ---------(1)

Here, L.P = $ 55, M = 25

Plugging the above values in (1)

(1)-----------> S.P = (100 - 25)% x 55

S.P = 75% x 55 ---------> S.P = 0.75 x 55

S.P = 41.25

Hence, the selling price is $ 41.25

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