A college student decides that school work limits him to a total of no more than 36
hours per week at his two parttime jobs. He earns $6 per hour hanging wall paper and
he has a sales job that pays $8 per hour. He needs to earn at least $245 per week to
cover his expenses. Write a system of inequalities that shows the various numbers of
hours he can work at each job. Let h represent the number of hours spent hanging wall
paper and let s represent the number of hours spent working at the sales job.
hours: h + s < or equal to 36
6h + 8s > or equal to 245
You can solve these just like you would equations.
How would you solve h + s = 36
6h + 8s = 245
Multiply the first equation by -6 and then combine the equations to eliminate the x and solve for y. Substitute back in to solve for x.
then go back to the original inequalities to find the various numbers houwer worked
well you would isolate y and i got s< or equal to -h+36
I meant to say s and h.
You could do that which issubstitution or you could use the addition/elimination method
-6h -6s <= 216
6h +8s >= 245
2s =461
To write a system of inequalities that represents the various numbers of hours the college student can work at each job, we need to consider the given conditions and information.
Let's start by defining the variables:
h = number of hours spent hanging wallpaper
s = number of hours spent working at the sales job
Now, let's establish the inequalities based on the given information:
1. The college student cannot work more than a total of 36 hours per week at both jobs. So, the sum of hours spent at each job should be less than or equal to 36:
h + s ≤ 36
2. The student earns $6 per hour hanging wallpaper. So, the total earnings from hanging wallpaper (6h) should be greater than or equal to zero:
6h ≥ 0
3. The student earns $8 per hour at the sales job. So, the total earnings from the sales job (8s) should be greater than or equal to zero:
8s ≥ 0
4. The student needs to earn at least $245 per week to cover expenses. So, the total earnings from both jobs combined (6h + 8s) should be greater than or equal to $245:
6h + 8s ≥ 245
Therefore, the system of inequalities representing the above conditions is:
h + s ≤ 36
6h ≥ 0
8s ≥ 0
6h + 8s ≥ 245
These inequalities describe the range of possible hours the student can work at each job while meeting the given conditions.