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Question

Part 1
The table shows the number of cell phone towers a company will build as the number of its customers increases. Complete a and b below.
Cell Phone Towers
Customers​ (thousands)
Towers
4.25
204
5.25
252
6.25
300
8.25
396
Question content area bottom
Part 1
a. Is the relationship between number of towers and number of customers​ proportional? Explain. Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
No. The ratios of towers to customers are not all equivalent.
B.
Yes. The ratios of towers to customers​ (thousands) are all equivalent to a unit rate of
  
StartFraction 48 Over 1 EndFraction
.
Your answer is correct.
Part 2
b. If there are 528 ​towers, how many customers does the company​ have? Write a proportion you can use to solve. Choose the correct proportion.
A.StartFraction 4 comma 250 Over 204 EndFraction equals StartFraction y Over 528 EndFraction
StartFraction 4 comma 250 Over 204 EndFraction equals StartFraction y Over 528 EndFraction
Your answer is correct.B.StartFraction 5.25 Over 300 EndFraction equals StartFraction y Over 528 EndFraction
StartFraction 5.25 Over 300 EndFraction equals StartFraction y Over 528 EndFraction
C.StartFraction 204 Over 4 comma 250 EndFraction equals StartFraction y Over 528 EndFraction
StartFraction 204 Over 4 comma 250 EndFraction equals StartFraction y Over 528 EndFraction
D.StartFraction 204 Over 4.25 EndFraction equals StartFraction y Over 528 EndFraction
StartFraction 204 Over 4.25 EndFraction equals StartFraction y Over 528 EndFraction
Part 3
The company has
  
enter your response here customers.
input field 1Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.Choose the correct proportion.The company hascustomers.input field 1Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.Choose the correct proportion.The company hascustomers.input field 1Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.Choose the correct proportion.The company hascustomers.

Answer 1

Let's analyze the information step-by-step.

Part 1

a. Is the relationship between the number of towers and the number of customers proportional? Explain.

To determine if the relationship is proportional, we need to calculate the ratios of towers to customers for each data point:

1. For 4.25 thousand customers:
   \[\frac{204}{4.25} = 48\]
2. For 5.25 thousand customers:
   \[\frac{252}{5.25} = 48\]
3. For 6.25 thousand customers:
   \[\frac{300}{6.25} = 48\]
4. For 8.25 thousand customers:
   \[\frac{396}{8.25} = 48\]

All ratios are equivalent to 48.

Thus, the correct answer is: B. Yes. The ratios of towers to customers are all equivalent to a unit rate of \(\frac{48}{1}\).

Part 2

b. If there are 528 towers, how many customers does the company have?

We can set up a proportion based on the established rate of towers to customers.

From earlier calculations, we can take one of the ratios, such as: \[ \frac{204}{4.25} = \frac{y}{528} \] Thus, the correct proportion is: A. \(\frac{4,250}{204} = \frac{y}{528}\)

Part 3

Now, let's solve the proportion \(\frac{204}{4.25} = \frac{y}{528}\).

First, we convert 4.25 to a more manageable number:

• \(4.25\) thousand customers is \(4250\) customers.

Now the proportion appears as: \[ \frac{204}{4250} = \frac{y}{528} \]

Cross-multiplying gives: \[ 204 * 528 = 4250 * y \] Calculating \(204 * 528\) gives: \[ 107,712 = 4250y \]

Now we can solve for \(y\): \[ y = \frac{107,712}{4250} \approx 25.3 \]

Since \(y\) must be in thousands of customers, we multiply this by 1000: \[ y \approx 25,300 \text{ customers} \]

Thus, the company has approximately 25,300 customers.