Question

In UITH, Dr Steve has worked more night shifts than Dr Greg who has worked five night shifts. Dr Okon has worked fifteen night shifts more than Dr Steve and Dr Greg combined. Dr Uche has worked eight night shifts less than Dr Steve. How many nights has Dr Steve worked?

Answer 1

Step-by-step explanation:

$g = 5 \\ o = g + s + 15 \\ u = s - 8$

Answer 2

Dr Steve has worked 2 night shifts.

Let's use variables to represent the number of night shifts each doctor has worked:

Let x be the number of night shifts worked by Dr Steve

Let y be the number of night shifts worked by Dr Greg

Then, Dr Steve has worked x night shifts, Dr Greg has worked y = 5 night shifts, and Dr Okon has worked x + y + 15 night shifts.

Also, Dr Uche has worked x - 8 night shifts.

We know that the total number of night shifts worked by all four doctors is:

x + y + (x + y + 15) + (x - 8) = 4x + 2y + 7

We also know that the total number of night shifts worked is the sum of the individual night shifts worked:

x + y + (x + y + 15) + (x - 8) = total number of night shifts worked

Substituting y = 5, we get:

x + 5 + (x + 5 + 15) + (x - 8) = total number of night shifts worked

Simplifying the expression, we get:

3x + 17 = total number of night shifts worked

We don't know the total number of night shifts worked, so we can't solve for x directly. However, we do know that each doctor must have worked a positive integer number of night shifts. We can use this fact to narrow down the possibilities for x.

First, we know that Dr Greg worked y = 5 night shifts, which means that x must be greater than 5. Next, we know that Dr Okon worked x + y + 15 night shifts, which means that x + y + 15 must be greater than 5. Substituting y = 5, we get:

x + 20 > 5

Simplifying the expression, we get:

x > -15

Since x is a positive integer, the smallest possible value for x is 1. Substituting x = 1, we get:

3(1) + 17 = 20

So if Dr Steve has worked one night shift, then the total number of night shifts worked is 20. But Dr Okon has worked x + y + 15 night shifts, which means that x + y + 15 must equal 19 or more. Since y = 5, the smallest possible value for x + y + 15 is:

1 + 5 + 15 = 21

So if Dr Steve has worked one night shift, then Dr Okon must have worked at least 21 night shifts. But Dr Okon has worked x + y + 15 night shifts, which means that x + y + 15 must equal 21 or more. Substituting y = 5, we get:

1 + 5 + 15 > 21

This inequality is not satisfied, which means that Dr Steve must have worked more than one night shift. We can try increasing x until we find a value that satisfies all of the constraints. Substituting x = 2, we get:

3(2) + 17 = 23

Dr Steve has worked two night shifts, then the total number of night shifts worked is 23. Dr Okon must have worked x + y + 15 night shifts, which means that x + y + 15 must equal 23 or more. Since y = 5, the smallest possible value for x + y + 15 is:

2 + 5 + 15 = 22

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