Answer each of the following questions.
a. 63 is 30% of what number?
b. What is 7% of 150?
c. 61.5 is what percent of 20.5?
d. 16 is 40% of what number?
Answer (2)
Find x such that 63 is 30% of x : x = 0.30 63 = 210 .
Calculate 7% of 150: 0.07 × 150 = 10.5 .
Find p such that 61.5 is p % of 20.5: p = 20.5 61.5 × 100 = 300 .
Find y such that 16 is 40% of y : y = 0.40 16 = 40 . The answers are 210 , 10.5 , 300 , 40 .
Explanation
Problem Overview We will solve each percentage problem step by step.
Solving for x a. We need to find the number x such that 63 is 30% of x . This can be written as: 0.30 x = 63 To find x , we divide both sides by 0.30: x = 0.30 63 = 210 So, 63 is 30% of 210.
Calculating 7% of 150 b. We need to find 7% of 150. This can be calculated as: 0.07 × 150 = 10.5 So, 7% of 150 is 10.5.
Finding the Percentage c. We need to find what percent 61.5 is of 20.5. Let p be the percentage. This can be written as: 100 p × 20.5 = 61.5 To find p , we multiply both sides by 100 and divide by 20.5: p = 20.5 61.5 × 100 = 20.5 6150 = 300 So, 61.5 is 300% of 20.5.
Solving for y d. We need to find the number y such that 16 is 40% of y . This can be written as: 0.40 y = 16 To find y , we divide both sides by 0.40: y = 0.40 16 = 40 So, 16 is 40% of 40.
Final Answers Therefore, the answers are: a. 63 is 30% of 210. b. 7% of 150 is 10.5. c. 61.5 is 300% of 20.5. d. 16 is 40% of 40.
Examples
Percentage calculations are used daily in various scenarios such as calculating discounts while shopping, determining interest on loans or savings, and understanding statistical data. For instance, if a store offers a 20% discount on an item priced at $50, you can calculate the savings by finding 20% of $50, which is $10. This means you would pay $40 for the item. Understanding percentages helps in making informed financial decisions and interpreting data effectively.
The calculations reveal that 63 is 30% of 210, 7% of 150 equals 10.5, 61.5 is 300% of 20.5, and 16 is 40% of 40.
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