Working his way through school, Joe works two part-time jobs for a total of 32 hours a week. Job A pays $6.00 per hour, and Job B pays $7.10 per hour. How many hours did he work at each job the week that he made $209.60?

Joe worked 16 hours at Job A and 16 hours at Job B the week he made $209.60, by solving a system of linear equations based on his total hours and earnings.

Explanation:

Joe works two part-time jobs for a total of 32 hours a week. Job A pays $6.00 per hour, and Job B pays $7.10 per hour. The week he made $209.60, we need to determine how many hours he worked at each job.

Step 1: Formulate the equations

Let x be the hours worked at Job A and y be the hours worked at Job B.
Therefore, the total hours equation is: x + y = 32
The total earnings equation from both jobs is: 6x + 7.10y = 209.60

Step 2: Solve the system of equations

Using the first equation, solve for y: y = 32 - x.

Substitute y in the earnings equation: 6x + 7.10(32 - x) = 209.60. Simplify and solve for x: x = 16.

Using x = 16, find y: y = 32 - 16, hence y = 16.

Joe worked 16 hours at each job the week he made $209.60.