DISCOUNTS AND MARKUPS

Discounts and markups are the common applications of percent change. 

Discounts

A discount is an amount by which an original price is reduced. 

Discount  =  Percent of original price

Final Price  =  Original price - Discount

Example 1 : 

Admission to a zoo is $7 and there is a discount of 20% for students. How much is the discount? How much should a student pay?

Solution : 

Method 1 :

A discount is a percent decrease. So find $7 decreased by 20%.

Find 20% of 7. This is the amount of the discount.

0.20(7)  =  1.40

Subtract 1.40 from 7. This is the student price.

7 - 1.40  =  5.60

Method 2 :

Subtract percent discount from 100%.

100% - 20%  =  80%

A student should pay 80% of the regular price, $7.

Find 80% of 7. This is the student price.

0.80(7)  =  5.60

Subtract 5.60 from 7. This is the amount of the discount.

7 - 5.60  =  1.40

By either method, the discount is $1.40 and student price is $5.60.

Example 2 : 

A $220 bicycle was on sale for 60% off. Find the sale price.

Solution : 

Subtract percent off from 100%.

100% - 60%  =  40%

The sale price is 40% of the regular price, $220.

Find 40% of 220. This is the sale price.

0.40(220)  =  88

The sale price of the bicycle is $88.

Example 3 : 

Ray paid $12 for a $15 T-shirt. What was the percent discount?

Solution : 

Amount of discount :

$15 - $12  =  $3

Think : 3 is what percent of 15? Let x represent the percent.

3  =  x(15)

Because x is multiplied by 15, divide each side by 15 to undo the multiplication.

3/15  =  15x/15

0.2  =  x

Multiply 0.2 by 100 to convert it to a percent. 

0.2 ⋅ 100%  =  x

20%  =  x

The discount is 20%.

Markups

A markup is an amount by which an original price is increased. 

Markup  =  Percent of wholesale cost

Final Price  =  Wholesale cost + Markup

Example 4 : 

Lorraine buys bangles at a wholesale cost of $50 each. He then marks up the price by 40% and sells the bangles. What is the amount of the markup? What is the selling price?

Solution : 

Method I :

A markup is a percent increase. So find $50 increased by 40%.

Find 40% of 50. This is the amount of the markup.

0.40(50)  =  20

Add to 50. This is the selling price.

50 + 20  =  70

Method II :

Add percent markup to 100%.

100% + 40%  =  140%

The selling price is 140% of the wholesale cost, $50.

Find 140% of 50. This is the selling price.

1.40(50)  =  70

Subtract the wholesale cost from 70. This is the amount of the markup.

70 - 50  =  20

By either method, the amount of the markup is $20 and the selling price is $70.

Example 5 : 

William bought an item for $80. The wholesale cost was $64. What was the percent markup?

Solution : 

Find the amount of the markup.

80 - 64  =  16

Think: 16 is what percent of 64? Let x represent the percent.

16  =  x(64)

Because x is multiplied by 64, divide each side by 64 to undo the multiplication.

16/64  =  64x/64

0.4  =  x

Multiply 0.4 by 100 to convert it to a decimal. 

0.4 ⋅ 100%  =  x

40%  =  x

The markup was 40%.

Example 6 : 

A video game has a 70% markup. The wholesale cost is $9. What is the selling price and the amount of the markup?

Solution : 

Add percent markup to 100%.

100% + 70%  =  170%

The selling price is 170% of the wholesale cost, $9.

Find 170% of 9. This is the selling price.

1.70(9)  =  15.3

Subtract the wholesale cost from 15.3. This oi the amount of mark up. 

15.3 - 9  =  6.3

The selling price is $15.30 and the amount of the mark up is $6.30.

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