If a painter charges $12 an hour and his son charges $6 an hour, how many hours did they work if their combined charge was $108?

• A. 6
• B. 9
• C. 12
• D. 18

Answer: (A)

To determine the number of hours the painter and his son worked based on their combined charge, we can set up an equation using their hourly rates.

Let ( x ) represent the number of hours the painter worked and ( y ) represent the number of hours his son worked. The painter charges $12 per hour, so his total charge would be ( 12x ), and the son charges $6 per hour, so his total charge would be ( 6y ). The combined charge they made is given as $108, leading us to the equation:

[ 12x + 6y = 108. ]

To simplify this equation, we can divide everything by 6:

[ 2x + y = 18. ]

Now, we need to find non-negative integer solutions for ( x ) and ( y ). We can express ( y ) in terms of ( x ):

[ y = 18 - 2x. ]

To satisfy the requirement that both ( x ) and ( y ) must be non-negative, we need:

[

18 - 2x \geq 0,

]

which simplifies to:

[

x \leq 9.