REWRITING PERCENT EXPRESSIONS

The stuff rewriting a percentage expression will help us to solve markup and markdown problems. 

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. 

Hints

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)% ⋅ 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)% ⋅ 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) ⋅ 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) ⋅ 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) ⋅ 100%

Examples

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 is 

=  Original cost + Markup

=  S + 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

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

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

So, the selling price is $35.

Example 4 : 

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

Substitute S.P  =  63 and M  =  40.    

63  =  (100 + 40)% x C.P 

63  =  140% x C.P

63  =  1.4 x C.P

Divide each side by 1.4.

45  =  C.P

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

Example 5 : 

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 %

So, the marked down rate is 25 %.

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