Question

Question content area top
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
238
5.25
294
6.25
350
8.25
462
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 56 Over 1 EndFraction
.
Your answer is correct.
Part 2
b. If there are 560 ​towers, how many customers does the company​ have? Write a proportion you can use to solve. Choose the correct proportion.
A.StartFraction 238 Over 4.25 EndFraction equals StartFraction y Over 560 EndFraction
StartFraction 238 Over 4.25 EndFraction equals StartFraction y Over 560 EndFraction
B.StartFraction 4 comma 250 Over 238 EndFraction equals StartFraction y Over 560 EndFraction
StartFraction 4 comma 250 Over 238 EndFraction equals StartFraction y Over 560 EndFraction
C.StartFraction 238 Over 4 comma 250 EndFraction equals StartFraction y Over 560 EndFraction
StartFraction 238 Over 4 comma 250 EndFraction equals StartFraction y Over 560 EndFraction
D.StartFraction 5.25 Over 350 EndFraction equals StartFraction y Over 560 EndFraction
StartFraction 5.25 Over 350 EndFraction equals StartFraction y Over 560 EndFraction

Answer 1

To solve the problem step by step:

**Part 1: a. Is the relationship between number of towers and number of customers​ proportional?**

To determine if the relationship is proportional, we need to check if the ratios of the number of towers to the number of customers (in thousands) are consistent across the data provided.

The ratios are:
1. For 4.25 (thousands of customers) and 238 towers:
Ratio = \( \frac{238}{4.25} = 56 \)

2. For 5.25 (thousands of customers) and 294 towers:
Ratio = \( \frac{294}{5.25} = 56 \)

3. For 6.25 (thousands of customers) and 350 towers:
Ratio = \( \frac{350}{6.25} = 56 \)

4. For 8.25 (thousands of customers) and 462 towers:
Ratio = \( \frac{462}{8.25} = 56 \)

Since all these ratios are equal (56), we conclude that the relationship is proportional.

**Answer: B. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of 56.**

---

**Part 2: b. If there are 560 towers, how many customers does the company have? Write a proportion you can use to solve.**

We will use the ratio of towers to customers to set up a proportion. Knowing from previous calculations that 238 towers correspond to 4.25 thousand customers, we can express it as:

\[
\frac{238 \text{ towers}}{4.25 \text{ thousand customers}} = \frac{560 \text{ towers}}{y \text{ thousand customers}}
\]

Looking at the options provided, the correct proportion that matches this setup is:

**Answer: A.** \( \frac{238}{4.25} = \frac{y}{560} \)

---

To find \( y \), cross-multiply and solve for \( y \):

\[
238 \cdot 560 = 4.25 \cdot y
\]

Calculating this will give you the number of customers in thousands (y). Then you can convert y back into the actual number of customers by multiplying by 1,000 since y is in thousands.