Let's start by defining some variables to represent the unknowns in the problem:
- Let's call the number of late slips that Robert issued "x".
- Since Robert took twice as many phone messages as late slips, he must have taken 2*× phone messages.
- Let's call the number of absentee reports that Robert entered "y".
From the problem statement, we know that Robert had a total of 18 tasks during the period, so we can write:
× + 2*× + y = 18
Simplifying this equation, we get:
3*× + y = 18
We also know that it takes Robert an average of 4 minutes to take a message, 1 minute to issue a late slip, and 5 minutes to enter an absentee report. So the total time he spent on these tasks can be expressed as:
4*(2*×) + 1*× + 5*y
Simplifying this expression, we get:
8*× + × + 5*y = 9*× + 5*
Now we can use the two equations we have to solve for x and y:
3*× + y = 18 (equation 1)
9*× + 5* = total time spent on tasks (equation 2)
To solve for x and y, we can use substitution or elimination. Let's use substitution:
From equation 1, we can solve for y:
y = 18 - 3*x
Substituting this into equation 2, we get:
9*× + 5*(18 - 3*×) = 9*x + 90 - 15*x
Simplifying this expression, we get:
-6*× + 90
Now we can solve for x:
-6*× + 90 = total time spent on tasks
× = (total time spent on tasks - 90)/ (-6)
Next, we can use this value of x to find
у:
y= 18 - 3*x
Finally, we can add up the time Robert spent on each task to find the total time he worked:
total time worked = 4* (2*×* (minutes spent taking phone messages) + ×* (minutes spent issuing late slips) + 5** (minutes spent entering absentee reports)
Plugging in the values we found for x and y, we get:
total time worked = 4* (2*x) + × + 5*y
total time worked = 4* (2* ((total time
spent on tasks