Question

c. use the values from the table to justify that the relationship between the amount of money received and the number of candy bars sold is proportional.

d. what does the point (0, 0) mean in this context?

1. logan and shawn recorded how much money they earned working at a local restaurant over a 5 - hour shift. use the tables shown for parts (a) and (b).

money logan earned
number of hours worked 1 2 3 4 5
money earned (dollars) 10 16 31 48 57

money shawn earned
number of hours worked 1 2 3 4 5
money earned (dollars) 9.50 19 28.50 38 47.50

practice

Explanation:

Step1: Recall proportional - relationship definition

A relationship is proportional if the ratio of the two quantities is constant. Let \(y\) be the money earned and \(x\) be the number of hours worked. The ratio is \(\frac{y}{x}\).

Step2: Calculate ratios for Shawn's data

For \(x = 1,y=9.50\), \(\frac{y}{x}=\frac{9.50}{1}=9.50\); for \(x = 2,y = 19\), \(\frac{y}{x}=\frac{19}{2}=9.50\); for \(x = 3,y=28.50\), \(\frac{y}{x}=\frac{28.50}{3}=9.50\); for \(x = 4,y = 38\), \(\frac{y}{x}=\frac{38}{4}=9.50\); for \(x = 5,y=47.50\), \(\frac{y}{x}=\frac{47.50}{5}=9.50\). Since the ratio \(\frac{y}{x}\) is constant (\(9.50\)), the relationship between the amount of money received and the number of hours worked for Shawn is proportional.

Step3: Analyze the point \((0,0)\)

In the context of money earned and hours worked, the point \((0,0)\) means that if \(0\) hours are worked, \(0\) dollars are earned.

Answer:

c. For Shawn, the ratios of money earned to hours worked are all \(9.50\), so the relationship is proportional.
d. It means that if \(0\) hours are worked, \(0\) dollars are earned.