A young woman wants to make at least $200 a week and can work no more than 30 hours a week. She works at the library for $8 an hour and babysits for $6 an hour.
a. What system of inequalities shows the possible combination of hours and jobs she can work?
b. Why did you exclude points to the left of the
a.
To find: the system of inequalities that show the possible combination of hours and jobs, the woman can work
Answer to Problem 5STP
The system of inequalities is as follows:
Here,
Explanation of Solution
Given information: A young woman wants to make at least
First find the inequality regarding total number of hours she works in a week.
Let
As she works for no more than
Now find the second inequality regarding total amount earned by her a week.
Amount earned by her per hour at the library
Amount earned by her in
Amount earned by her per hour from babysitting
Amount earned by her in
So,
Total amount earned by her
Also, it’s given that she wants to make at least
So,
b.
To explain: reason behind excluding points to the left of y-axis and below the x-axis.
Answer to Problem 5STP
Points to the left of y-axis and below the x-axis are excluded as number of hours cannot be negative.
Explanation of Solution
x-axis denotes number of hours she works at the library and y-axis denotes number of hours she does babysitting.
Here, number of hours she works at the library and number of hours she does babysitting cannot be negative.
As time cannot be negative, points to the left of y-axis and below the x-axis are excluded as number of hours cannot be negative.
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