Mathematics
Grade 10
15 min
Percent of a number: tax, discount, and more
Percent of a number: tax, discount, and more
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1
Introduction & Learning Objectives
Learning Objectives
Calculate the final price of an item after applying a single percentage discount or tax.
Solve multi-step problems involving sequential percentages, such as a discount followed by a tax.
Determine the original price of an item given the final price and the percentage change (reverse percentages).
Calculate percent increase and decrease in various contexts, including profit, loss, and commission.
Apply percentage calculations to solve real-world financial literacy problems, including simple interest and gratuity (tips).
Formulate and solve algebraic equations to represent percentage problems.
Analyze and compare different percentage-based scenarios to make informed financial decisions.
Ever seen a '50% off, then an extra 20% off' sale and wonde...
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Key Concepts & Vocabulary
TermDefinitionExample
PercentA ratio expressed as a fraction of 100. The word 'percent' literally means 'per hundred'.50% is equivalent to the fraction 50/100 or the decimal 0.5.
Sales TaxA percentage of the selling price of a good or service that is added to the cost.A 7% sales tax on a $20 item adds $1.40 ($20 * 0.07) to the price, making the total $21.40.
DiscountA reduction in the usual price of an item, typically expressed as a percentage.A 25% discount on an $80 jacket saves you $20 ($80 * 0.25), making the sale price $60.
CommissionA fee paid to an agent or employee for transacting a piece of business or performing a service, often calculated as a percentage of the sale amount.A real estate agent earning a 3% commission on a $300,000 house sale makes $9,000.
Gra...
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Core Formulas
Calculating a Percentage of a Number
\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}
Use this fundamental formula to find a specific percentage of a given total amount. 'Percent' is the number (e.g., 25 for 25%), and 'Whole' is the original number.
Final Price with Tax/Discount
\text{Final Price} = \text{Original Price} \times (1 \pm \frac{\text{Percent}}{100})
A shortcut to find the final price. Use '+' for a percentage increase (like tax or tip) and '-' for a percentage decrease (like a discount). For example, a 15% discount is calculated by multiplying by (1 - 0.15) = 0.85.
Reverse Percentage Calculation
\text{Original Price} = \frac{\text{Final Price}}{(1 \pm \frac{\text{Percent}}{100})}
Use this to find the or...
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Challenging
Store A offers a 30% discount on a $500 camera. Store B offers the same camera with a 20% discount, followed by an additional 15% discount on the sale price. Which store offers a better final price, and by how much?
A.Store A, by $10
B.Store B, by $10
C.Store A, by $20
D.Their prices are the same.
Challenging
A coat is sold for $240, which represents a 25% profit on the cost price for the store. If the store owner wanted to make a 40% profit instead, what should the selling price have been?
A.$256
B.$268.80
C.$336
D.$250
Challenging
The price of a stock was increased by p%. Later, the new price was decreased by p%. If the final price was 96% of the original price, what is the value of p?
A.4
B.16
C.20
D.2
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