Question

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week.

Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work.
Graph the inequalities.
What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain.

Answer 1

Alright well we know she MUST work at least 5 hours at the restaurant at 8 dollars an hour

On top of that she does yard work for 12 an hour

So all in all she works (restaurant hours + yard work hours) and we dont want that to exceed 15 right?

And she also makes 8 per hour at the restaurant and 12 per hour doing yard work...


Lets let Yard Work = Y
And Restaurant = R

So

Hours:

\[\large R + Y \le 15\]
Right? because the total hours between restaurant working and yard work cannot go over 15

And Money:
\[\large 8R + 12Y \ge 120 \]
Right? because the 8 dollars per restaurant hour worked + 12 dollars per yard hours worked would be at or over the 120 she wants

Answer 2

So the system of equations

\[\large R + Y \le 15\]
\[\large 8R + 12Y \ge 120\]

Answer 3

omg thank you!

Answer 4

No problem...and when you graph it...and see where the graphs overlap...you will have your solution :)

Answer 5

thanks! it helped a lot!!

Answer 6

Anytime hun :)