Answer :
Final answer:
Robert worked 10 hours at Job A, which paid $6.40 per hour, and 14 hours at Job B, which paid $6.70 per hour, making a total of $157.80 for the week.
Explanation:
Calculating Hours Worked at Each Job
Robert works two part-time jobs for a total of 24 hours a week. Job A pays $6.40 per hour, and Job B pays $6.70 per hour. He made a total of $157.80 in one week. To find out how many hours he worked at each job, we can set up the following system of equations:
Let x represent the hours worked at Job A, and y represent the hours worked at Job B. The first equation represents the total hours worked:
1. x + y = 24
The second equation represents the total amount earned:
2. 6.40x + 6.70y = 157.80
Solving this system of equations gives us:
- Multiply the entire first equation by -6.40 to set up for elimination with the second equation:
- -6.40x - 6.40y = -153.60
- Add this new equation to the second equation to eliminate x:
- 0.30y = 4.20
- Now, solve for y:
- y = 4.20 / 0.30
- y = 14
- Substitute y = 14 into the first equation to find x:
- x + 14 = 24
- x = 24 - 14
- x = 10
Therefore, Robert worked 10 hours at Job A and 14 hours at Job B.