Question

You worked a total of 200 hours this summer at the local restaurant. Some of the time you worked as a waiter, which pays $6 per hour, and some of the time you were a cook, which pays $8 per hour. You made $1300 over the summer. How many hours did you work each job?

Answer 1

The student worked 150 hours as a waiter and 50 hours as a cook over the summer. We derived this by creating a system of equations using the provided pay rates and total earnings, and then solving for the number of hours in each job.

Step-by-step explanation:

To solve the problem about how many hours a student worked as a waiter and how many as a cook, we need to create a system of equations based on the information given:

1. The student worked a total of 200 hours over the summer.
2. The student worked some hours as a waiter at $6 per hour and some as a cook at $8 per hour.
3. The student made a total of $1300 over the summer.

Let w be the number of hours worked as a waiter and c be the number of hours worked as a cook. We can then express the situation with the following equations:

w + c = 200

6w + 8c = 1300

To solve this system, we can use either the substitution or the elimination method. For illustration, we will use the substitution method:

1. Express w in terms of c from the first equation:
   w = 200 - c.
2. Substitute this expression for w into the second equation:
   6(200 - c) + 8c = 1300.
3. Simplify and solve for c:
   1200 - 6c + 8c = 1300
   2c = 100
   c = 50.
4. Now substitute c = 50 into the expression for w:
   w = 200 - 50
   w = 150.

So, the student worked 150 hours as a waiter and 50 hours as a cook.