Question
The sum of two numbers is 76 . Express the product of the numbers, \( P \), as a function of one of the numbers, \( x \). \( 62.57 \%, 65.7 \) of \( P(x)=\square \) Save points Soints: 0 of 2
Ask by Cruz Higgins. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( P(x) = x(76 - x) \)
Solution
To express the product of two numbers, \( P \), as a function of one of the numbers, \( x \), given that their sum is 76, follow these steps:
1. **Identify the Two Numbers:**
- Let one number be \( x \).
- Since their sum is 76, the other number will be \( 76 - x \).
2. **Express the Product \( P \):**
\[
P(x) = x \times (76 - x)
\]
3. **Simplify the Expression (Optional):**
\[
P(x) = 76x - x^2
\]
**Final Function:**
\[
P(x) = x(76 - x) \quad \text{or} \quad P(x) = 76x - x^2
\]
This function represents the product of the two numbers in terms of \( x \).
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Simplify this solution Extra Insights
Let's express the product \( P \) of the two numbers based on their given sum of 76. If we let one number be \( x \), the other number can be expressed as \( 76 - x \). The product of the two numbers can then be written as: \[ P(x) = x(76 - x) = 76x - x^2. \] So the function for the product is \( P(x) = 76x - x^2 \). Now, how does this apply in real life? Imagine you're planning an event and need to coordinate the number of tables and chairs. Understanding the relationship of two variables and maximizing their product (in this case, space used) can help optimize your layout. Using the formula helps you visualize and organize effectively for a fantastic setup!
