*I'll be reviewing a*

**New York State Regents Exam**Question every day from now until the Regents exams next week. At least, that is the plan.### August 2014, Questions 37

**37.** *Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.
Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below.
*

*Determine and state one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours.*

If one job pays $4 per hour and she works *x* hours, she makes *4x* dollars. If the other job pays $8 per hour and she works *y* hours, then she makes *5y* dollars. The total is *4x + 8y*, which must be greater than or equal to $80, so
**4x + 8y > 80**

If the total number of hours worked about both jobs must be less than or equal to 15 hours, then
**x + y < 15**

That is the **system of inequalities** to graph. Both lines will be solid. The one for her pay will be shaded above. The one for her hours will be shaded below.

You can graph these by finding the x- and y-intercepts, or by re-writing them in y-intercept form and putting them in the graphing calculator.

4x = 80 x = 20, (20, 0) |
8y = 80 y = 10, (0, 10) |
x = 15, (15, 0) |
y = 15, (0, 15) |

The answer to the second part varies. You can pick any part in the double-shaded region, S. Since the lines are solid, those boundary points are good as well.

So 0 hours babysitting and 10 hours at the library, or 3 hours babysitting and 9 hours at the library.

See image below.

Any questions?

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.

## 1 comment:

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