Hi i'm having trouble with a question. it states During the Summer you take 2 part time jobs. The first job pays $5 per hour. The 2nd Job pays $8 per hour. You want to earn at least $150 a week and work 25 hours or less a week.
Write a system of inequalities that model the hours you can work at each Job.
with x = hours at first job
and y = hours at the second job
y <= 25 - x
which is the amount of hours you can work
at the same time,
y >= (150/8)- (5/8)x
is the amount of money you want to make
if you graph both of these equations, you can find the range you should use.
To write a system of inequalities that models the hours you can work at each job, we need to consider the following conditions:
1. The total amount you earn each week should be at least $150.
2. The total number of hours you work each week should be 25 or less.
Let's denote the number of hours you work at the first job as "x", and the number of hours you work at the second job as "y".
1. The total amount you earn each week can be calculated by multiplying the number of hours worked by the pay rate for each job and adding them together. Therefore, the first inequality is:
5x + 8y ≥ 150
2. The total number of hours you work each week should be 25 or less. Therefore, the second inequality is:
x + y ≤ 25
Combining these two inequalities gives the system:
{
5x + 8y ≥ 150,
x + y ≤ 25
}
This system of inequalities models the hours you can work at each job while ensuring you earn at least $150 a week and work 25 hours or less.