Question

You can work at most 20 hours next week. You need to earn at least $92 to cover your weekly expenses. Your dog-walking job pays $7.50 per hour and your job as a car wash attendant pays $6 per hour. Write a system of linear inequalities to model the situation.

Answer 1

Please help! Medal will earned for your assistance. Thanks!

Answer 2

@jim_thompson5910

Answer 3

I was out on the day when my teacher taught the assignment/lesson to class. Please help me through this problem.

Answer 4

Let's use x and y as our variables.

x = amount of hours worked as a dog walker
y = amount of hours worked as a car wash attendant


based on the info `You can work at most 20 hours next week` what inequality can we form?

Answer 5

7.50x+6y>or equal to 92

Answer 6

I am not sure if this is correct...

Answer 7

do you agree that `x+y` is the total amount of hours worked overall?

Answer 8

Yes

Answer 9

so if `You can work at most 20 hours next week` then this is the ceiling or max you can work

giving us this inequality `x+y <= 20`

Answer 10

the total `x+y` must be less than 20 hrs or equal to 20 hrs. You cannot exceed 20 hrs

Answer 11

Ok, I see

Answer 12

hopefully that makes sense? that wraps up the first inequality

Answer 13

That makes so much sense now! Ok, so it will be 7.50x+6<=92 right?

Answer 14

` so it will be 7.50x+6<=92 right?` very close

Answer 15

6y

Answer 16

`7.50x+6y<=92` is closer but still not the right inequality

Answer 17

"You need to earn AT LEAST $92"

Answer 18

Ok

Answer 19

"at least" means that amount or more

Answer 20

>=

Answer 21

so $92 is the lowest amount you are willing to earn

Answer 22

yes, `7.50x+6y>=92`

Answer 23

Ok thank you. Do you mind if you can help me through some more problems please?

Answer 24

so the system of inequalities is

\[\Large \begin{cases}x+y\le20\\7.5x+6y\ge92\end{cases}\]

Answer 25

Oh, so there is suppose to be two equations? Ok, I see.

Answer 26

you can also throw in that x >= 0 and y >= 0 to basically say "x and y can't be negative" so here is a more extended system

\[\Large \begin{cases}x+y\le20\\7.5x+6y\ge92\\x\ge0\\y\ge0\end{cases}\]

Answer 27

Thank you!

Answer 28

no problem

Answer 29

`Do you mind if you can help me through some more problems please?`
if you have other questions, post them seperately one at a time (one question per post). Then you can tag me or any other helper on the site

to tag a person, type the @ sign then the user name

so here is me tagging you @Kaylea_Knighton