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.
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.
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]
- The total number of hours worked per week is 24 hours. Thus, the first equation is:
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]
- First, solve one of the equations for one variable. We'll solve the first equation for [tex]y[/tex]:
Therefore, Blake worked 13 hours at Job A and 11 hours at Job B that week.