Joseph and Hunter worked as plumbers for $36 and $40 per hour, respectively. In January, Joseph worked eighteen hours more than Hunter. If their total income for January was $5,968, how many hours did Hunter work?
Let's start by setting up two equations. Let j be the number of hours Joseph worked and h be the number of hours Hunter worked.
j = h + 18 (Joseph worked eighteen hours more than Hunter)
36j + 40h = 5968 (Their total income for January was $5,968)
Now we can substitute the first equation into the second equation to eliminate j:
36(h+18) + 40h = 5968
Distribute the 36:
36h + 648 + 40h = 5968
Combine like terms:
76h + 648 = 5968
Subtract 648 from both sides:
76h = 5320
Divide both sides by 76:
h = 70
So Hunter worked 70 hours in January. To find out how many hours Joseph worked, we can substitute h=70 into the first equation:
j = h + 18 = 70 + 18 = 88
So Joseph worked 88 hours in January.
Let's assume that Hunter worked x hours in January.
Joseph worked 18 hours more than Hunter, so he worked x + 18 hours in January.
The hourly rate for Joseph is $36, so his total income is 36 * (x + 18).
The hourly rate for Hunter is $40, so his total income is 40 * x.
Their total income for January was $5,968.
So, we can write the equation:
36 * (x + 18) + 40 * x = 5,968.
Now we can solve this equation to find the value of x, which represents the number of hours Hunter worked.