Final answer:
The nail cost 5 cents, and the hammer cost $1.05 since it is one dollar more expensive than the nail. The correct equation to use is x + (x + $1.00) = $1.10, where x represents the cost of the nail.
Step-by-step explanation:
To solve the problem where you bought a hammer and a nail for $1.10, and the hammer costs one dollar more than the nail, we need to set up an equation. Let's denote the cost of the nail as x dollars. The cost of the hammer would therefore be x + $1.00 (one dollar more than the nail). According to the problem, the total cost is $1.10, which gives us the following equation:
x + (x + $1.00) = $1.10
Simplifying the equation, we combine like terms:
2x + $1.00 = $1.10
Subtract $1.00 from both sides of the equation to isolate the terms with x:
2x = $0.10
Finally, divide both sides by 2 to solve for x:
x = $0.05
So, the nail cost 5 cents, and the hammer cost $1.05 since it costs one dollar more than the nail.