If operating expenses are 40% of revenue, by what percentage does revenue exceed operating expenses?

If operating expenses are 40% of revenue, then revenue can be expressed as:

\[
\text{Operating Expenses} = 0.40 \times \text{Revenue}
\]

Let $ R $ represent revenue and $ E $ represent operating expenses. Thus, we have:

\[
E = 0.40R
\]

We need to determine by what percentage revenue exceeds operating expenses. This is calculated by the formula:

\[
\text{Percentage by which revenue exceeds expenses} = \left( \frac{R - E}{E} \right) \times 100
\]

Substitute $ E = 0.40R $ into the formula:

\[
\text{Percentage} = \left( \frac{R - 0.40R}{0.40R} \right) \times 100
\]

Simplifying the expression:

\[
\text{Percentage} = \left( \frac{0.60R}{0.40R} \right) \times 100 = \left( \frac{0.60}{0.40} \right) \times 100 = 1.5 \times 100 = 150\%
\]

Thus, **revenue exceeds operating expenses by 150%**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. What is the relationship between profit and revenue if expenses are 40% of revenue?
2. How would changes in operating expenses affect the percentage by which revenue exceeds expenses?
3. If operating expenses increase to 50% of revenue, what is the new percentage by which revenue exceeds expenses?
4. What would the revenue be if operating expenses were $20,000 and they are 40% of revenue?
5. How can a business reduce the percentage of revenue spent on operating expenses?

**Tip:** Always double-check percentage calculations to ensure they align with the desired comparison (e.g., how much one value exceeds another).

Understand how to calculate the percentage by which revenue exceeds operating expenses when expenses are 40% of revenue. This step-by-step guide uses key algebraic concepts and percentage calculations, making it suitable for students in Grades 8-10.

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