Each morning, a deli worker has to make several pies and peel a bucket of potatoes.
- On Monday, it took the worker 2 hours to make the pies and an average of 1.5 minutes to peel each potato.
- On Tuesday, the worker finished the work in the same amount of time, but it took 2.5 hours to make the pies and an average of 1 minute to peel each potato.
About how many potatoes are in a bucket?
- What quantities do you know and how are they related to each other?
- How can you use the known and unknown quantities to write an equation for this situation?
Answer (3)
Let the number of Potatoes = P
On Monday the time spent was 2 hours + 1.5*P minutes Convert the time to make the pies into minutes = 120 minutres Therefore on Monday the worker took
120 + 1.5P minutes
On Tuesday the worker took 2.5 hours (150 minutes) + 1minute x P ie 150 + P minutes
We are told that the times are the same therefore 120 + 1.5P = 150 + P subtract P from both sides of the equation 120 + 0.5P = 150 Subtract 120 from both sides of the equation 0.5P = 30
Therefore P = 30/0.5 = 60
There are 60 potatoes in the bucket.
By setting up an equation that represents the total work time on both Monday and Tuesday and solving for the number of potatoes 'P', we find that the bucket contains approximately 60 potatoes.
To determine how many potatoes are in a bucket, we must set up an equation based on the given information. On Monday, the worker spent 2 hours making pies and the rest of the time peeling potatoes. Since the total work time was the same on both days, we can conclude that the total time spent on Tuesday (2.5 hours on pies) plus the time spent peeling potatoes equaled the total time spent on Monday. We'll use the variable 'P' to represent the number of potatoes in the bucket.
On Monday, the worker spent 1.5 minutes per potato, peeling 'P' potatoes after making pies for 2 hours. On Tuesday, it took the worker 1 minute per potato after 2.5 hours making pies. Since both days had the same total work time, we can create the following equation to represent the situation:
2 hours + (1.5 minutes/potato) * P = 2.5 hours + (1 minute/potato) * P
Converting the work-hours into minutes to match the potato peeling times (since 1 hour = 60 minutes), we get:
120 minutes + (1.5 minutes/potato) * P = 150 minutes + (1 minute/potato) * P
Now, we can solve for 'P' by isolating the variable on one side of the equation:
(1.5 minutes/potato - 1 minute/potato) imes P = 150 minutes - 120 minutes
0.5 minute/potato * P = 30 minutes
P = 30 minutes / (0.5 minute/potato)
P = 60 potatoes
Therefore, there are about 60 potatoes in a bucket according to the given values.1
After setting up equations based on time spent making pies and peeling potatoes, it was determined that there are 60 potatoes in the bucket. This was calculated by equating the total time for both days and solving for the variable representing the number of potatoes. The resulting equation led to the conclusion that P = 60.
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