# CALCULATING MARKUPS AND MARKDOWNS WORKSHEET

Problem 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 ?

Problem 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.

Problem 3 :

On selling 20 units of an item, the profit is equal to cost price of 5 units. Find the mark mark up rate.

Problem 4 :

Difference between the cost price of two products is \$10. Difference between the selling price is \$20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

Problem 5 :

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

Problem 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

Problem 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

Problem 3 :

On selling 20 units of an item, the profit is equal to cost price of 5 units. Find the mark mark up rate.

Solution :

Let m be the cost price of one unit.

Then, we have

Cost price of 5 units  =  5m

Cost price of 20 units  =  20m

Given : On selling 20 units of an item, the profit is equal to cost price of 5 units.

Then, we have

Profit  on selling 20 units  =  C.P of 5 units  =  5m

Mark up rate  =  (profit / cost) ⋅ 100%

Mark up rate  =  (5m / 20m) ⋅ 100%

Mark up rate  =  (1 / 4) ⋅ 100%

Mark up rate  =  25%

Problem 4 :

Difference between the cost price of two products is \$10. Difference between the selling price is \$20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

Solution :

Let x and y be the cost prices of two products.

Then, we have

x - y  =  10 -----(1)

Let us assume that x is sold at 20% profit.

Then, the selling price of x is

=  120% ⋅ x

=  1.2x

Let us assume that y is sold at 20% loss.

Then, the selling price of y is

=  80% ⋅ y

=  0.8y

Given : Difference between the selling price is \$20

1.2x - 0.8y  =  20

Multiply each side by 10.

12x - 8y  =  200

Divide each side by 4.

3x - 2y  =  50 -----(2)

Solving (1) and (2), we get

x  =  30

y  =  20

So, the cost prices of the two products are \$30 and \$20.

Problem 5 :

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  is \$120.

Let x be the selling price.

From the above picture, we get

90% of (M.P)  =  x

(0.9) ⋅ 120  =  x

108  =  x

Therefore, the selling price is \$108.

Cost price  =  \$100

Selling Price  =  \$108

Mark up rate  =  8%

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