Question

1. the table shows the number of cell phone towers a company will build as the number of its customers increases.

part a
is the relationship between number of towers and number of customers proportional? explain.
part b
if there are 576 towers, how many customers does the company have? write a proportion you can use to solve.

1. select all true statements about the table at the right.

the table shows a proportional relationship.
when x is 20, y is 2.55.
all the ratios $\frac{y}{x}$ for related pairs of x and y are equivalent to 8.
the unit rate of $\frac{y}{x}$ for related pairs of x and y is $\frac{1}{8}$.
if the table continued, when x is 30, y would be 3.75.
106 2 - 3 understand proportional relationships: equivalent ratios

Explanation:

Step1: Calculate ratios for Part A

For the first pair: $\frac{252}{5.25}=48$. For the second pair: $\frac{300}{6.25} = 48$. For the third pair: $\frac{348}{7.25}=48$. For the fourth pair: $\frac{444}{9.25}=48$. Since the ratio of number of towers to number of customers is constant ($48$), the relationship is proportional.

Step2: Set up proportion for Part B

Let the number of customers be $x$ (in thousands). The proportion is $\frac{48}{1}=\frac{576}{x}$. Cross - multiplying gives $48x = 576$, so $x=\frac{576}{48}=12$ (in thousands), so the company has $12000$ customers.

Step3: Analyze statements in 15

For the table with $x$ and $y$ values:

• Calculate $\frac{y}{x}$ for each pair: $\frac{1.5}{12}=\frac{1}{8}$, $\frac{2.25}{18}=\frac{1}{8}$, $\frac{2.75}{22}=\frac{1}{8}$, $\frac{3.25}{26}=\frac{1}{8}$. So the table shows a proportional relationship and the unit rate of $\frac{y}{x}$ is $\frac{1}{8}$.
• If $x = 20$, then $y=\frac{1}{8}\times20 = 2.5

eq2.55$.

• If $x = 30$, then $y=\frac{1}{8}\times30 = 3.75$.

The true statements are:

• The table shows a proportional relationship.
• The unit rate of $\frac{y}{x}$ for related pairs of $x$ and $y$ is $\frac{1}{8}$.
• If the table continued, when $x$ is $30$, $y$ would be $3.75$.

Answer:

Part A: Yes, the relationship is proportional because the ratio of number of towers to number of customers is constant ($48$).
Part B: The proportion is $\frac{48}{1}=\frac{576}{x}$, and the company has $12000$ customers.
15: The table shows a proportional relationship; The unit rate of $\frac{y}{x}$ for related pairs of $x$ and $y$ is $\frac{1}{8}$; If the table continued, when $x$ is $30$, $y$ would be $3.75$.