A bottle and its cork together cost $1.10. The bottle costs exactly $1.00 more than the cork. How much does the cork cost?
Correct: $0.05
Let B represent the cost of the bottle and C represent the cost of the cork.
From the problem, we have two equations:
1. B + C = $1.10 (The total cost of the bottle and cork)
2. B = C + $1.00 (The bottle costs $1.00 more than the cork)
Many people incorrectly assume the cork costs $0.10. If the cork cost $0.10, then the bottle would cost $1.00 more, which is $1.10. Adding these together ($1.10 + $0.10) gives $1.20, not $1.10. This shows the common guess is incorrect.
To solve correctly, substitute the second equation into the first equation:
(C + $1.00) + C = $1.10
Combine the 'C' terms:
2C + $1.00 = $1.10
Subtract $1.00 from both sides of the equation:
2C = $1.10 - $1.00
2C = $0.10
Divide by 2 to find the cost of the cork:
C = $0.10 / 2
C = $0.05
So, the cork costs $0.05. This means the bottle costs $0.05 + $1.00 = $1.05. Together, $1.05 (bottle) + $0.05 (cork) = $1.10, which matches the problem statement.