Applying Discounts and Markups
Applying Discounts and Markups is a Grade 7 math skill in Illustrative Mathematics, Chapter 4: Proportional Relationships and Percentages. Students calculate sale prices after discounts and selling prices after markups by applying percentage changes to original values.
Key Concepts
Let $P O$ be the original price, $d$ be the discount rate, and $m$ be the markup rate.
The Sale Price ($P S$) after a discount is: $$P S = P O \times (1 d)$$ The Retail Price ($P R$) after a markup is: $$P R = P O \times (1 + m)$$ To find the Original Price from the Sale Price: $$P O = \frac{P S}{1 d}$$.
Common Questions
How do you calculate a discount?
Multiply the original price by the discount percentage (as a decimal) to find the discount amount, then subtract from the original price. Or multiply by (1 minus the discount rate).
How do you calculate a markup?
Multiply the original cost by the markup percentage (as a decimal) to find the markup amount, then add to the original cost. Or multiply by (1 plus the markup rate).
What is the formula for a discounted price?
Sale Price equals Original Price times (1 minus discount rate). For example, a $40 item with a 25% discount: 40 times 0.75 equals $30.
What is the formula for a marked-up price?
Selling Price equals Cost times (1 plus markup rate). For example, a $20 item with a 50% markup: 20 times 1.5 equals $30.
What chapter covers discounts and markups in Illustrative Mathematics Grade 7?
Discounts and markups are covered in Chapter 4: Proportional Relationships and Percentages in Illustrative Mathematics Grade 7.