Question

the table shows the number of cell phone towers a company will build as the number of its
cell phone towers
b. if there are 728 towers, how many customers does the company have? write a proportion you can use to solve. choose the correct proportion.
a. \\( \frac { 5,250 } { 294 } = \frac { y } { 728 } \\)
b. \\( \frac { 294 } { 5,250 } = \frac { y } { 728 } \\)
c. \\( \frac { 294 } { 5.25 } = \frac { y } { 728 } \\)
d. \\( \frac { 6.25 } { 406 } = \frac { y } { 728 } \\)
the company has \\( \square \\) customers.

Explanation:

Step1: Analyze the proportion relationship

We assume that the ratio of customers to cell - phone towers is constant. From the table (assuming the first row has 5250 customers and 294 towers), the proportion should be \(\frac{\text{customers}_1}{\text{towers}_1}=\frac{\text{customers}_2}{\text{towers}_2}\). Let \(y\) be the number of customers when there are 728 towers. So \(\frac{5250}{294}=\frac{y}{728}\).

Step2: Solve the proportion for \(y\)

Cross - multiply the proportion \(\frac{5250}{294}=\frac{y}{728}\). We get \(294y = 5250\times728\). Then \(y=\frac{5250\times728}{294}\).
First, simplify \(\frac{5250}{294}=\frac{5250\div42}{294\div42}=\frac{125}{7}\).
Now, \(y=\frac{125\times728}{7}\). Since \(728\div7 = 104\), then \(y=125\times104\).
\(125\times104=125\times(100 + 4)=125\times100+125\times4=12500 + 500=13000\).

Answer:

A. \(\frac{5250}{294}=\frac{y}{728}\), The company has \(13000\) customers.