Question

A juice factory offers its juice in both bottles and cans. A class of students on a field trip decides to compare the numbers of cases of bottled juice and canned juice that are packaged each minute. The students count the number of cases that are packaged on each assembly line over several minutes. Time. Cases(minutes) Packeged 2 92 3. 138 4. 184. 1. What is the unit rate for bottled juice, in cases per minute? Explain how you found this unit rate.2. What is the unit rate for canned juice, in cases per minute? Explain how you found this unit rate.3. Are cans or bottles Packeged at a faster rate explain your answer

Answer 1

We can find the rate of change, given two data points, with the following formula:

`m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)`

1)Given the information on the table, we can use the points (2,92) and (4,184) to find the rate of change:

`\begin{gathered} (x_1,y_1)=(2,92) \\ (x_2,y_2)=(4,184) \\ \Rightarrow m=(184-92)/(4-2)=(92)/(2)=46 \\ m=46 \end{gathered}`

thus, we have that the unit rate for bottled juice is 46 casesper minute.

B)Notice that on the graph, we can see that the two points (1,50) and (2,100) are on the line, then, we can use this information to find the rate of change:

`\begin{gathered} (x_1,y_1)=(1,50) \\ (x_2,y_2)=(2,100)_{} \\ \Rightarrow m=(100-50)/(2-1)=(50)/(1)=50 \\ m=50 \end{gathered}`

then, we have that the unit rate for canned juice is 50 cases per minute

C)Clearly, from both rates, we can see that the canned juice are packaged at a faster rate than the bottled juice cases, since the unit rate is greater for the canned juice cases