the number of bottles a machine is proportional to the number of minutes the machine operates the machine fills 250 bottles every 20 minutes 0,0 to 10,125 explain why these are the answers
To understand why the answers are as given, let's first analyze the information provided and the relationship between the number of bottles and the number of minutes the machine operates.
According to the problem statement, the number of bottles filled by the machine is proportional to the number of minutes it operates. This means that as the number of minutes increases, the number of bottles filled also increases at a consistent rate.
We are given that the machine fills 250 bottles in 20 minutes. To find the proportionality constant, we can set up a proportion using this information.
Let's denote the number of bottles as 'B' and the number of minutes as 'M.' We have the following proportion:
B/250 = M/20
Now let's use this proportion to find the number of bottles for a range of minutes. We can choose a few different values of 'M' and calculate the corresponding number of bottles, 'B':
For 'M = 0':
B/250 = 0/20
B = 0
For 'M = 10':
B/250 = 10/20
B = 125
Therefore, when the machine operates for 10 minutes, it fills 125 bottles.
Similarly, we can calculate for 'M = 5':
B/250 = 5/20
B = 62.5
However, since we are considering whole numbers of bottles, we can round down this value to get the answer:
When the machine operates for 5 minutes, it fills 62 bottles.
Applying the same procedure for various values of 'M' between 0 and 10, we can determine the number of bottles filled by the machine in that corresponding time frame. Here are the results:
(M, B)
(0, 0)
(1, 12.5) => Rounded down to 12
(2, 25)
(3, 37.5) => Rounded down to 37
(4, 50)
(5, 62)
(6, 75)
(7, 87.5) => Rounded down to 87
(8, 100)
(9, 112.5) => Rounded down to 112
(10, 125)
Hence, the given answers (0, 0) to (10, 125) represent the number of bottles filled by the machine as it operates between 0 and 10 minutes.
To determine why the answers are 0,0 and 10,125, we need to understand the given information that the number of bottles a machine fills is proportional to the number of minutes the machine operates.
We are given that the machine fills 250 bottles every 20 minutes. This means that for every 20 minutes the machine operates, it fills 250 bottles. We can use this information to find the constant of proportionality.
Let's set up a proportion:
Number of bottles = Constant of proportionality × Number of minutes
250 bottles = k × 20 minutes
To find the constant of proportionality, we can solve for k:
k = 250 bottles / 20 minutes
k = 12.5 bottles per minute
Now we have the constant of proportionality, which means we can calculate the number of bottles for any given number of minutes.
For the first part, when 0 minutes have passed, the machine has not operated yet. Therefore, it has not filled any bottles, resulting in the answer 0,0.
For the second part, when 10 minutes have passed, we can calculate the number of bottles filled by multiplying the number of minutes by the constant of proportionality:
Number of bottles = k × Number of minutes
Number of bottles = 12.5 bottles per minute × 10 minutes
Number of bottles = 125 bottles
So, when the machine operates for 10 minutes, it fills 125 bottles, resulting in the answer 10,125.