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 C be the cost of the cork and B be the cost of the bottle.
From the first statement, we know: B + C = $1.10.
From the second statement, we know: B = C + $1.00.
Now, 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:
2C = $0.10
Divide by 2:
C = $0.05
So, the cork costs $0.05, and the bottle costs $1.05 ($0.05 + $1.00). Together, they cost $1.05 + $0.05 = $1.10.