Cathy’s customer base is ( 2)/(3) residential and ( 1)/(3) business. If she has 350 residential customers, how many total customers does she have? 235 425 525 None of the above. Explain it.
The Correct Answer and Explanation is :
To determine Cathy’s total number of customers, we can use the information that her customer base is divided into two-thirds residential and one-third business. Given that she has 350 residential customers, we can set up the following equation:
[
\frac{2}{3} \times \text{Total Customers} = 350
]
To find the total number of customers, we solve for it by dividing both sides of the equation by two-thirds:
[
\text{Total Customers} = \frac{350}{\frac{2}{3}} = 350 \times \frac{3}{2} = 525
]
Therefore, Cathy has a total of 525 customers.
Explanation:
- Understanding the Fractional Distribution:
- Cathy’s customer base is divided into two-thirds residential and one-third business. This means that for every three customers, two are residential, and one is business.
- Setting Up the Equation:
- Let the total number of customers be represented by ( T ).
- Since two-thirds of the total customers are residential, we can express this relationship as:
[
\frac{2}{3} \times T = 350
] - Here, 350 represents the number of residential customers.
- Solving for the Total Number of Customers:
- To isolate ( T ), divide both sides of the equation by two-thirds:
[
T = \frac{350}{\frac{2}{3}} = 350 \times \frac{3}{2} = 525
] - This calculation shows that the total number of customers is 525.
- Verification:
- To verify, calculate one-third of 525:
[
\frac{1}{3} \times 525 = 175
] - Since the business customers make up one-third, there are 175 business customers.
- Adding the residential and business customers:
[
350 \, (\text{residential}) + 175 \, (\text{business}) = 525
] - This confirms that the total number of customers is indeed 525.
Conclusion:
By understanding the fractional distribution of Cathy’s customer base and applying basic algebraic principles, we determined that Cathy has a total of 525 customers. This method ensures accuracy and provides a clear understanding of how the total is derived from the given information.