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?
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 :
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:
- `13.5x+16.5y = 352.5`
- `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`
Now we can find x from any one of our previous equations. So use the easiest
`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