SOLUTION: Systems of Equations and Inequalities Suppose you have a job at a restaurant that pays $12 per hour. You also work at a bookstore that pays $9 per hour. You want to earn a

Question 434346: Systems of Equations and Inequalities

Suppose you have a job at a restaurant that pays $12 per hour. You also work at a bookstore that pays $9 per hour. You want to earn at least $225 per week, but would like to work no more than 25 hours per week.
a. Write a system of linear inequalities that describes this situation.
b. Determine the solutions to the system. Explain what each solution to the system represents.

I was thinking that I need to have a problem equation something like this:
x+y=25
9x+12y=225
This is as far as I can get. Can you show me where I am going wrong and how to proceed.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Suppose you have a job at a restaurant that pays $12 per hour.
You also work at a bookstore that pays $9 per hour.
You want to earn at least $225 per week, but would like to work no more than 25 hours per week.
:
a. Write a system of linear inequalities that describes this situation.
:
This is right, but should be written as an inequality
x + y =< 25
9x+12y=>225
:
Use the 1st equation for substitution in the 2nd equation
y = (25-x)
9x + 12(25-x) => 225
9x + 300 - 12x => 225
9x - 12x => 225 - 300
-3x => -75
Multiply by -1, to get rid of the negatives, this reverses the inequality sign
3x =< 75
x =<
x =< 25 hrs at the book store,
:
If you worked all 25 hr at the book store you would just make $225
Less than 25 hrs, you would work the remaining hr at the restaurant and make more than $225
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