Direction: Solve the following.
The Correct Answer and Explanation is:
Here are the correct answers for the ten percentage problems:
- P = 4.86
- R = 50%
- B = 12,250
- P = 10.35
- R = 25%
- B = 32
- R = 20%
- P = 11
- P = 80
- B = 20
To solve these problems, we rely on the fundamental formula in percentage calculations: P = B × R, where P is the percentage value (also called the part), B is the base (the whole or reference amount), and R is the rate (expressed as a decimal when multiplying).
To find any missing value, we rearrange the formula appropriately:
- If P and B are known, find R using R = P ÷ B
- If P and R are known, find B using B = P ÷ R
- If B and R are known, find P using P = B × R
For instance, in problem 1, we are given R as 18% and B as 27. We convert 18% to decimal form, which becomes 0.18. Then multiply: P = 27 × 0.18 = 4.86
In problem 3, we are given P and R. To isolate B, we divide: B = 2,450 ÷ 0.20 = 12,250
This approach builds algebraic fluency and reinforces proportional reasoning. The problems also improve your ability to switch between percentage, decimal, and whole-number representations. Practicing these conversions is essential in economics, chemistry (like concentration calculations), and statistics where ratios and proportions are common.
Overall, this worksheet strengthens numerical intuition and prepares you for advanced applications, including marginal analysis and error detection in applied mathematics.
