Write an expression for each day's work and then equate them.
60 potatoes
Practice makes perfect
We have been asked to calculate the number of potatoes in a bucket. Let's begin by answering the questions posed.
Known Quantities
From the problem we know the amount of time it took the deli worker to complete the pies on each day, as well as the rate at which the potatoes were peeled. Let's write the relationship as an equation.
Time=Pies+Rate* Number of potatoes
Unknown Quantities
The unknown value is the number of potatoes. The known values are the times to make pies and the rates to peel potatoes. First, we need to find the product of the number of potatoes p and the rates.
1.5p and 1p
Then we add the respective time to make pies to each of these. Since it took the same total time on both days, these expressions can then be set equal to one another to form an equation.
Solve the Problem
We are assuming that a bucket roughly holds the same number of potatoes each day, p. Since we have two different time units, we need to choose which unit to work with. For simplicity, let's use minutes.
Phrase
Expression
2 hours to make pies on Monday
2 hours = 120 minutes
1.5 minutes to peel each potato on Monday
1.5p
2.5 hours to make pies on Tuesday
2.5 hours = 150 minutes
1 minute to peel each potato on Tuesday
1p
Now we can write an expression describing how many minutes the deli worker took to complete the work on Monday.
120+1.5p
Next we can write an expression for the number of minutes the deli worker took on Tuesday.
150+p
Since the total amount of time for both days was the same, we can form an equation by setting the two expressions equal to each other.
120+1.5p= 150+p
From there we solve for p to find the number of potatoes. To do this we will use the inverse operations.
