This exam was adminstered in June 2025.
June 2025 Algebra, Part IV
A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.
35. Sarah earns $6 per hour babysitting and $12 per hour tutoring. Her goal is to earn at least $120
per week. Sarah is allowed to work a maximum of 14 hours per week doing both jobs.
If x represents the number of hours Sarah babysits and y represents the number of hours she
tutors, write a system of inequalities that could model this situation.
On the set of axes below, graph the system of inequalities that you wrote.
State a combination of hours babysitting and tutoring that would satisfy this situation.
Justify your answer.
Answer:
Write two inequalities in Standard form. If you can graph from Standard Form, GREAT! If not, solve each inequality for y and use your graphing calculator to assist you.
Sarah can work a maximum of 14 hours, so the total of x and y must be less than or equal to 14.
The amount she earns is $6 times x hours plus $12 times y hours, and she wants this to be at least (that is, greater than or equal to) $120.
Both inequalities are solid lines. The first will be shaded beneath the line, and the second will be shaded above the line.
Sarah can work anywhere from 14 hours babysitting and 0 hours tutoring to 0 hours babysitting and 14 hours tutoring. You can plot these two points and draw the line.
Or you can rewrite the inequality as y = 14 - x, and graph a line with a slope of -1 and a y-intercept of 14.
The second inequality has an x-intercept (y=0) of 6x = 120 or x = 20 and a y-intercept (x=0) of 12y = 120 or y = 10.
You can rewrite the inequality as 12y > -6x + 120 or y > -1/2 x + 10
Your graph should look something like this:
You can pick any solution in the double-shaded area, but you have to answer the question. DO NOT give a pair of coordinates.
For example: 2 hours of babysitting and 10 hours of tutoring.
Justification: 2 + 10 < 14; 12 < 14; check.
6(2) + 12(10) > 120; 132 > 120; check.
End of Exam
How did you do?
Questions, comments and corrections welcome.
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