High School

Blake is working his way through school. He works two part-time jobs for a total of 24 hours a week. Job A pays $6.20 per hour, and Job B pays $7.20 per hour. How many hours did he work at each job the week that he made $159.80?

Job A:

Job B:

Answer :

To solve the problem of determining how many hours Blake worked at each job, we can set up a system of equations based on the information given.

  1. Identify the variables:

    • Let [tex]x[/tex] be the number of hours Blake worked at Job A.
    • Let [tex]y[/tex] be the number of hours Blake worked at Job B.

  2. Set up the equations:

    • The total number of hours worked per week is 24 hours. Thus, the first equation is:
      [tex]x + y = 24[/tex]
    • The total earnings for the week is $159.80. Earnings from Job A is [tex]6.20x[/tex], and from Job B is [tex]7.20y[/tex]. Thus, the second equation is:
      [tex]6.20x + 7.20y = 159.80[/tex]

  3. Solve the system of equations:

    • First, solve one of the equations for one variable. We'll solve the first equation for [tex]y[/tex]:
      [tex]y = 24 - x[/tex]
    • Substitute [tex]y = 24 - x[/tex] into the second equation:
      [tex]6.20x + 7.20(24 - x) = 159.80[/tex]
    • Simplify and solve for [tex]x[/tex]:
      [tex]6.20x + 172.80 - 7.20x = 159.80[/tex]
      [tex]-1.00x + 172.80 = 159.80[/tex]
      [tex]-1.00x = 159.80 - 172.80[/tex]
      [tex]-1.00x = -13.00[/tex]
      [tex]x = 13[/tex]
    • Now, substitute [tex]x = 13[/tex] back into the equation for [tex]y[/tex]:
      [tex]y = 24 - 13[/tex]
      [tex]y = 11[/tex]

Therefore, Blake worked 13 hours at Job A and 11 hours at Job B that week.

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