Sharyn worked as registered nurse in London last summer.The first week she was there she worked a total of 23 hours at a city hospital. She was paid $13.50 an hour for day shift and $16.50 an hour...

Sharyn worked as registered nurse in London last summer.The first week she was there she worked a total of 23 hours at a city hospital. She was paid $13.50 an hour for day shift and $16.50 an hour for night shift work.She earned $352.50 for her first week of work.

How many hours did she spend on the day shift? How many hours did she spend on the night shift?

Expert Answers
durbanville eNotes educator| Certified Educator

You need to create a system of equations to nable you to interpret this information.

Let x= day shift hours and Let y = night shift hours

We know she worked 23 hours in the first week so we know :

`x+y=23`

We also know that she earned $13,50 for each day shift hour so that is 13,50x  and $16,50 for night shift so that is 16,50x.

We know that all her hours added together (ie 13,50x + 16,50y) earned her $352,50 so we know :

`13.5x + 16.5y = 352.5` (we can drop the extra zeros)

which is the same as

`13.50x + 16.50 y = 352.50`

Now we have a system of equations. Because we have 2 unknowns (x and y) we needed 2 equations. Now we can solve them simultaneously:

  1. `13.5x+16.5y = 352.5`
  2. `x+y = 23`  

Multiply equation 2. by (-  13.5) so that we can remove one of the unknowns. You could also have multiplied 2. by  (- 16.5) and eliminated y first if that is what you prefer.

   3.  `- 13.5x - 13.5y = 23 times 13.5`

Now take 3. away from 1.

`0 x + 3y =42`

`therefore y=42/3=14`

Now we can find x from any one of our previous equations. So use the easiest

`x+y=23`

`x+14 = 23`

`therefore x=23 - 14 = 9`

Now x is the number of day shift hours and y is the number of night shift hours

Therefore she worked 9 day shift hours and 14 night shift hours