Not sure if I'm retaining this correctly

Question

You are a supervisor in a hospital in charge of nurse's shift. You have 29 weekends shifts and 61 weekdays shifts to distribute among three Nursing stations (trauma, pediatric care, and maternity.) The maternity station need twice as many shifts as the trauma station on weekdays, but the same number of shifts on weekends. To cover necessary task, the pediatric care station needs one more shift than the trauma station on weekdays but four less shifts than trauma on weekends. How should the shifts be distribute among the stations?

Answer 1

The best way for me to help you with this problem is similar to the parable 'give a man a fish and you feed him for a day. teach a man how to fish and you feed him for a lifetime'. I am a test preparation expert and one of the greatest advantages of the ACT is that it provides you the correct answer on every question! (except essay) It is not worth your time to figure out exactly how to do this problem because you are not likely to be able to use that on your actual test. Knowing about ratios will be helpful of course, but most important would be to develop estimating skills and using the answers to your advantage. There may even be some obvious trap answers you could eliminate without any work. The answer is Maternity: 41 (30+11), Trauma 26 (15+11) and Pediatric 23 (16+7). The first # listed in () is step one. If the answers were given, I feel very confident that step one, with some common sense, would be the most you would need to get the answer correct.

Answer 2

Dear Keshia,

Just for the record, your use of the word "retaining" is incorrect. However, let's focus on the math. A big trick is the ability to translate English sentences into mathematical sentences, in this case, equations.

We need to consider the weekday shifts separately from the weekend shifts. We need to express the number of maternity and pediatric shifts in terms of the number of trauma shifts. First, however, let's define some unknowns, using logical letter choices.

T: # of weekday trauma shifts

M: # of weekday maternity shifts

P: # of weekday pediatric shifts

We know that the total number of weekday shifts is 61.

We can say that: T + M + P = 61

We also can express M and P in terms of T.

M= 2T

P = T + 1

Now we substitute these expressions of M and P in the above equation: T + M + P = 61.

T + M + P = 61

T + 2T + (T + 1) = 61

Combine like terms to get

T + 2T + T + 1 = 61

4T + 1 = 61

4T + 1 –1 = 61 – 1

4T = 60

T = 15

So, on weekdays, the trauma station needs 15 shifts, the maternity station needs twice that or 30 shifts, and the pediatric station needs one more than 15 or 16 shifts. If you add 15, 16, and 30, you get 61, the number of weekday shifts.

You can do something similar for the weekend shifts. I will start it for you, and I'm sure that you can finish it.

TT: # of weekend trauma shifts

MM: # of weekend maternity shifts

PP: # of weekend pediatric shifts

MM = TT

PP = TT – 4

TT + MM + PP = 29

TT + TT + (TT – 4) = 29

I'll let you take it from here. Good luck and let me know if you need more help!!!