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:
-
For 4.25 (thousands of customers) and 238 towers:
Ratio = \( \frac{238}{4.25} = 56 \) -
For 5.25 (thousands of customers) and 294 towers:
Ratio = \( \frac{294}{5.25} = 56 \) -
For 6.25 (thousands of customers) and 350 towers:
Ratio = \( \frac{350}{6.25} = 56 \) -
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.
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