Question 542424: Linda works at a pharmacy for $15 an hour. She also babysits for $10 an hour. Linda needs to earn at least $90 per week, but she does not want to work more than 20 hours per week. Show and describe the number of hours Linda could work at each job to meet her goals. List two possible solutions.
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!
Let our two variables be:
p # of pharmacy hours
b # of babysitting hours
Then we should have two statements from the given facts:
 and 
We can graph these inequalities by solving for either p or b in both inequality.
Once the inequalities are graphed then any point that is shaded in their intersection will work.
We can also throw out any negative points on the graph since hours worked can't be less than zero.
So our graph would only be "meaningful" in Quadrant I.
The easiest solutions to find are when one job takes up all the hours per week, and the other job gets no hours:
If p=20, then b=0, and she makes 20*15 dollars, or 300 dollars.
If p=0, then b=20, and she makes 20*10 dollars, or 200 dollars.
Both of these solutions satisfy the given inequalities.
If she can work a partial number of hours, such as 7.2 hours (real numbers) at any one job, then there is an INFINITE amount of solutions.
If she can only work full hours (integer values), then there is definitely a finite amount of solutions.
I hope this helps!
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