High School

Working his way through school, 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. How many hours did he work at each job the week that he made $157.80? (Round to two decimal places if necessary.)

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:

  1. Multiply the entire first equation by -6.40 to set up for elimination with the second equation:
  2. -6.40x - 6.40y = -153.60
  3. Add this new equation to the second equation to eliminate x:
  4. 0.30y = 4.20
  5. Now, solve for y:
  6. y = 4.20 / 0.30
  7. y = 14
  8. Substitute y = 14 into the first equation to find x:
  9. x + 14 = 24
  10. x = 24 - 14
  11. x = 10

Therefore, Robert worked 10 hours at Job A and 14 hours at Job B.

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