SOLUTION: My question is: J is weighing his options between 2 jobs. Job 1 pays an hourly wage of $7. Job 2 pays $5 an hour plus a flat rate of $20 per week. *Write the linear function for e

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: My question is: J is weighing his options between 2 jobs. Job 1 pays an hourly wage of $7. Job 2 pays $5 an hour plus a flat rate of $20 per week. *Write the linear function for e      Log On


   

Question 60701: My question is: J is weighing his options between 2 jobs. Job 1 pays an hourly wage of $7. Job 2 pays $5 an hour plus a flat rate of $20 per week.
*Write the linear function for each job.
*Graph each function (let x represent the hours worked).
*At which point (time in hours) will his wage be the same (what is the amount)?
*If J's goal is to earn $100 per week, what is the minimum number of hours he must work at each job?
Please help me because I am confused on how to specifically graph each linear function!!! Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
My question is: J is weighing his options between 2 jobs. Job 1 pays an hourly wage of $7. Job 2 pays $5 an hour plus a flat rate of $20 per week.
*Write the linear function for each job.
Let y = amt earned, x = hrs worked:
:
job 1:
y = 7x
:
job 2
y = 5x + 20
:
*Graph each function (let x represent the hours worked)
I assume you know how to plot a graph from the equations (I will explain it if you don't).
Job 1 is red, job 2 is green
+graph%28+300%2C+200%2C+-5%2C+20%2C+-10%2C+120%2C+7x%2C+5x%2B20%29+
:
*At which point (time in hours) will his wage be the same (what is the amount)?
You can see that in the graph where the lines intersect, however, you can easily calculate too. When the 1st equation = the 2nd equation:
7x = 5x + 20
7x - 5x = 20
2x = 20
x = 10 hrs the two hours will be equal, right?
:
*If J's goal is to earn $100 per week, what is the minimum number of hours he must work at each job?
Let's add one more equation to the graph: y = 100
+graph%28+300%2C+200%2C+-5%2C+20%2C+-10%2C+120%2C+7x%2C+5x%2B20%2C+100%29+
You can see the values of x above horizontal line, will give the hrs required for each job earn $100 or more
:
However, we can calculate this too. Substitute 100 for y in both equations:
7x = 100
x = 100/7
x = 14.28 so must work 15 hr in job 1
:
5x + 20 = 100
5x = 100 -20
5x = 80
x = 16 hrs in job 2 to make $100
:
Make sense to you? Any questions?