Discounts and markups are the common applications of percent change.
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?
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.
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?
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%.
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?
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?
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?
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.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
Negative exponents rules
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Ratio and proportion shortcuts
Converting repeating decimals in to fractions