If the cost and revenue funcation of a product are respectively `C(x) = 5x + 700` and `R(x) = 15 x + 100` , where `x` is the number of products then what will be the value of `x` to get profit ?

Explanation

To determine the value of \( x \) that results in a profit, we start by defining the profit in terms of the cost and revenue functions.

1. **Identify the Cost and Revenue Functions:**
- Cost function: \( C(x) = 5x + 700 \)
- Revenue function: \( R(x) = 15x + 100 \)

2. **Define Profit:**
- Profit occurs when revenue exceeds cost. Therefore, we need to set up the inequality:
\[ R(x) > C(x) \]

3. **Substitute the Functions into the Inequality:**
- Substitute \( R(x) \) and \( C(x) \) into the inequality:
\[ 15x + 100 > 5x + 700 \]

4. **Rearrange the Inequality:**
- To isolate \( x \), we first subtract \( 5x \) from both sides:
\[ 15x - 5x + 100 > 700 \]
- This simplifies to:
\[ 10x + 100 > 700 \]

5. **Isolate the Variable:**
- Next, subtract 100 from both sides:
\[ 10x > 700 - 100 \]
- This simplifies to:
\[ 10x > 600 \]

6. **Solve for \( x \):**
- Finally, divide both sides by 10:
\[ x > 60 \]

7. **Conclusion:**
- The value of \( x \) must be greater than 60 for the company to make a profit. Thus, the solution is:
\[ x > 60 \]