Application: Half Price Sale
Apply percent algebra to half-price sale problems in Grade 9. Calculate discounts, find sale prices, and solve percentage equations by writing and solving algebraic expressions.
Key Concepts
Property Real world problems can be modeled with complex expressions. Use symbols of inclusion to group costs, apply discounts, and calculate a final total. For example, to find the remaining money, subtract the total cost from the initial amount: Money [Total Cost].
Examples $50 \text{ dollars} [\frac{2 \cdot 10 \text{ dollars}}{2} + \frac{3 \cdot 15 \text{ dollars}}{2}] = 50 [10 + 22.50] = 50 32.50 = 17.50 \text{ dollars}$.
Explanation Math helps you shop smarter! This problem uses brackets to group all your purchases and discounts together. It calculates the final bill first, then subtracts it from the money you have. This way, you know exactly how much cash you'll have left for a celebratory soda!
Common Questions
How do you calculate a 50% discount algebraically?
Multiply the original price by 0.5 or divide by 2 to find the sale price. To find the original price from the sale price, divide by 0.5.
What is the formula for finding a sale price after a percentage discount?
Sale price = Original price × (1 - discount rate). For a 30% discount: Sale price = Original × 0.70. Subtract the discount percentage from 100% and convert to a decimal.
How do you find the original price when you know the sale price and discount?
Divide the sale price by (1 - discount rate). If something costs $24 after a 40% discount: original = 24 / 0.60 = $40. Solve the equation x × 0.60 = 24 algebraically.