College

You have two jobs. One job pays $7 per hour, and the other pays $8.25 per hour. You worked a total of 22 hours last week and earned $171.50. How many hours did you work at each job?

Answer :

x = 1st job
y = 2nd job

x + y = 22......x = 22 - y
7x + 8.25y = 171.50

7(22 - y ) + 8.25y = 171.50
154 - 7y + 8.25y = 171.50
-7y + 8.25y = 171.50 - 154
1.25y = 17.50
y = 17.50 / 1.25
y = 14 <== 14 hrs at the 8.25 per hr job

x + y = 22
x + 14 = 22
x = 22 - 14
x = 8 <=== 8 hrs at the 7 per hr job

The student worked 8 hours at the job paying $7 per hour and 14 hours at the job paying $8.25 per hour, which was determined by setting up and solving a system of equations based on the total hours worked and the earnings from both jobs.

To solve the problem of determining how many hours were worked at each job, we need to set up a system of equations based on the information provided. Let's denote x as the number of hours worked at the job paying $7 per hour and y as the number of hours worked at the job paying $8.25 per hour.

System of Equations Setup

We are given that the total number of hours worked across both jobs is 22, so we have:

x + y = 22 (1)

We also know that the total earnings from both jobs are $171.50, and if we multiply the number of hours worked by the hourly rates and add them together, we get:

7x + 8.25y = 171.50 (2)

Solving the System of Equations

  1. Solve equation (1) for x: x = 22 - y

  2. Substitute the expression for x from equation (1) into equation (2): 7(22 - y) + 8.25y = 171.50

  3. Simplify and solve for y:

    154 - 7y + 8.25y = 171.50

    1.25y = 17.50

    y = 14

  4. Substitute y = 14 back into equation (1) to solve for x:

    x = 22 - 14

    x = 8

Conclusion

The student worked 8 hours at the job paying $7 per hour and 14 hours at the job paying $8.25 per hour.

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