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.

Question

Cell Phone Towers
Customers​ (thousands)
Towers
4.25
187
5.25
231
6.25
275
8.25
363
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.
Yes. The ratios of towers to customers​ (thousands) are all equivalent to a unit rate of
  
StartFraction 44 Over 1 EndFraction
.
Your answer is correct.B.
No. The ratios of towers to customers are not all equivalent.
Part 2
b. If there are 440 ​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 187 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 4 comma 250 Over 187 EndFraction equals StartFraction y Over 440 EndFraction
B.StartFraction 5.25 Over 275 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 5.25 Over 275 EndFraction equals StartFraction y Over 440 EndFraction
C.StartFraction 187 Over 4 comma 250 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 187 Over 4 comma 250 EndFraction equals StartFraction y Over 440 EndFraction
D.StartFraction 187 Over 4.25 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 187 Over 4.25 EndFraction equals StartFraction y Over 440 EndFraction

Answer 1

To answer the questions about the relationship between the number of cell phone towers and the number of customers, let's analyze the provided data.

Part 1

a. To determine if the relationship is proportional, we can compare the ratios of towers to customers for each case. Let's calculate these ratios:

1. For 4.25 thousand customers: $$\text{Ratio}=\frac{187}{4.25}$$ Calculation: $$\frac{187}{4.25}=\frac{187\times 100}{425}=\frac{18700}{425}\approx 44$$

2. For 5.25 thousand customers: $$\text{Ratio}=\frac{231}{5.25}$$ Calculation: $$\frac{231}{5.25}=\frac{231\times 100}{525}=\frac{23100}{525}\approx 44$$

3. For 6.25 thousand customers: $$\text{Ratio}=\frac{275}{6.25}$$ Calculation: $$\frac{275}{6.25}=\frac{275\times 100}{625}=\frac{27500}{625}\approx 44$$

4. For 8.25 thousand customers: $$\text{Ratio}=\frac{363}{8.25}$$ Calculation: $$\frac{363}{8.25}=\frac{363\times 100}{825}=\frac{36300}{825}\approx 44$$

Since all ratios are approximately equal to 44, the answer is:

A. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of $\frac{44}{1}$.

Part 2

b. To find out how many customers correspond to 440 towers, we can use a proportion that relates the number of towers to the number of customers.

Let's use the first data point from the table for our proportion: $$\frac{4,250\text{ customers}}{187\text{ towers}}=\frac{y\text{ customers}}{440\text{ towers}}$$

Thus, the correct proportion is:

A. $\frac{4,250}{187}=\frac{y}{440}$

Summary of Answers:

• Part 1: A. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of $\frac{44}{1}$.
• Part 2: A. $\frac{4,250}{187}=\frac{y}{440}$