Math Problem Statement

If A's salary is 15% more than B's, then what percent B's salary is less than A's?

Solution

Let's denote B's salary as BB and A's salary as AA.

Given that A's salary is 15% more than B's salary, we have: A=B+0.15B=1.15BA = B + 0.15B = 1.15B

Now, we want to find what percent B's salary is less than A's. To do this, we calculate the difference between A's and B's salaries and express it as a percentage of A's salary:

Difference=AB=1.15BB=0.15B\text{Difference} = A - B = 1.15B - B = 0.15B

The percentage by which B's salary is less than A's is given by: Percentage=(0.15BA)×100\text{Percentage} = \left(\frac{0.15B}{A}\right) \times 100

Substituting A=1.15BA = 1.15B into the formula: Percentage=(0.15B1.15B)×100=(0.151.15)×10013.04%\text{Percentage} = \left(\frac{0.15B}{1.15B}\right) \times 100 = \left(\frac{0.15}{1.15}\right) \times 100 \approx 13.04\%

Thus, B's salary is approximately 13.04% less than A's salary.

Would you like more details on this calculation or have any further questions?

Here are 5 related questions for further practice:

  1. If B's salary is $50,000, what is A's salary?
  2. If A's salary is 20% more than B's, what percent is B's salary less than A's?
  3. If A's salary is $69,000 and it's 15% more than B's, what is B's salary?
  4. What is the percentage difference between A's and B's salaries if A's salary is 25% more than B's?
  5. If B's salary is 10% less than A's, by what percentage is A's salary more than B's?

Tip: When comparing percentages in both directions (A to B and B to A), the percentages will differ because the base (denominator) changes.

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Math Problem Analysis

Mathematical Concepts

Percentage
Arithmetic Operations

Formulas

Percentage change formula

Theorems

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Suitable Grade Level

Grades 7-9