Question

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
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

Answer 1

To determine if the relationship between the number of towers and the number of customers is proportional, let’s calculate the ratios of towers to customers based on the provided data:

- For 4.25 thousand customers:
\[
\text{Ratio} = \frac{204}{4.25} \approx 48
\]

- For 5.25 thousand customers:
\[
\text{Ratio} = \frac{252}{5.25} \approx 48
\]

- For 6.25 thousand customers:
\[
\text{Ratio} = \frac{300}{6.25} \approx 48
\]

- For 8.25 thousand customers:
\[
\text{Ratio} = \frac{396}{8.25} \approx 48
\]

Since all the ratios of towers to customers (approximately 48) are essentially equivalent, we can conclude that the relationship is proportional.

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

---

**Part 2**
To find how many customers correspond to 528 towers, we can use a proportion based on one of the already established ratios.

Using the first ratio:

\[
\frac{204 \text{ towers}}{4.25 \text{ thousand customers}} = \frac{528 \text{ towers}}{y \text{ thousand customers}}
\]

This matches option A. Therefore, the correct proportion is:

A. \( \frac{4,250}{204} = \frac{y}{528} \)