Percent Word Problems

Explanation

Percent word problems involve finding a percentage of a quantity, determining what percentage one number is of another, or calculating the total when a percentage is given. The key to solving these problems is to translate the words into mathematical equations using the concept of percentages.

Worked Example

Problem: A store is having a sale where all items are 25% off. If a jacket originally costs $80, what is the sale price?

Step 1: Convert the percentage to a decimal.

$$25\% = \frac{25}{100} = 0.25$$

Step 2: Calculate the discount amount.

$$\text{Discount} = \text{Original Price} \times \text{Decimal Percentage} = 80 \times 0.25 = 20$$

Step 3: Subtract the discount from the original price to find the sale price.

$$\text{Sale Price} = \text{Original Price} - \text{Discount} = 80 - 20 = 60$$

Answer: The sale price of the jacket is $60.

Key Questions

• If a car is priced at $20,000 and is discounted by 15%, what is the sale price?
• A student scored 18 out of 20 on a test. What percentage did the student score?
• If a shirt costs $30 after a 10% discount, what was the original price?
• If a population increases by 12% and the current population is 500, what will the new population be?
• A recipe calls for 40% sugar. If the total weight of the recipe is 200 grams, how much sugar is needed?

Keywords

• Percentage
• Discount
• Original Price
• Sale Price
• Increase