# 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?

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### 1 Answer

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:

- `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`

`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**

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