system of inequalities

Question

Edith babysits for x hours a week after school at a job that pays $4 an hour. She had accepted a job that pays $8 an hour as a library assistant woking 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 want 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.

Answer 1

Alodrona, Arthur showed you the system.  Here's why it's that way.

 

She can only work up to 15 hours a week in both jobs, so x hours babysitting plus y hours at the library can't add to more than 15.  How do we write that? See Arthur's first equation.

 

If she works 2 hours babysitting, she makes $4(2 hours) = $8.  Working x hours, she makes $4x.  The same goes for the y but she'd be making $8y at the library.  

 

She wants to make at least $80 a week working both jobs.  How do we write that?  See Arthur's second equation.

 

Let's say she works 5 hours babysitting and 3 hours at the library.  Then x = 5 and y = 3, right?

 

x + y < 15

5 + 3 < 15

      8 < 15

 

Hey, that's true, because 8 is less than 15.

 

4x + 8y > 80

4(5) + 8(3) > 80

20 + 24 > 80

44 > 80

 

Doesn't work, because 44 is less than 80.

 

There is a way to solve for what works as x and y, but you'll learn that another time!

Answer 2

x+y<15

4x+8y>80