SOLUTION: I have to solve using equations with two variables...Can you help me? Page 504 Number 5 Income of a nurse Sharyn worked as a Registered Nurse in London last summer. The firs

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Question 145186This question is from textbook Beginning Algebra
: I have to solve using equations with two variables...Can you help me?
Page 504
Number 5
Income of a nurse Sharyn worked as a 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 the day shift and $16.50 and hour for the 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? This question is from textbook Beginning Algebra

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Income of a nurse x + y = 23
worked as a 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 the day shift and $16.50 and hour for the 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?
.
.
Let x = hours worked in the day shift
and y = hours worked in the night shift
.
Since we have two unknowns, we'll need two equations.
.
Equation 1 can be derived from:
"The first week she was there she worked a total of 23 hours at a city hospital."
x + y = 23
.
Equation 2 can be derived from:
"She was paid $13.50 an hour for the day shift and $16.50 and hour for the night shift work. She earned $352.50 for her first week of work."
13.50x + 16.50y = 352.50
.
Using the substitution method, solve eq 1 for x:
x + y = 23
x = 23 - y
.
Substitute the above into eq 2 and solve for y:
13.50x + 16.50y = 352.50
13.50(23 - y) + 16.50y = 352.50
310.5 - 13.50y + 16.50y = 352.50
310.5 + 3y = 352.50
3y = 352.50 - 310.5
3y = 42
y = 14
.
Substitute the above into eq 1 and solve for x:
x + y = 23
x + 14 = 23
x = 23 - 14
x = 9
.
Therefore, Sharyn worked:
9 hrs. in the day shift
14 hrs. in the night shift