Bunuel
A hotel purchased a number of hand towels and a number of bath towels. If the cost of each hand towel was $6.00 and the cost of each bath towel was $11.00, what was the total cost of the hand towels and bath towels purchased by the hotel?
(1) The total cost of the hand towels purchased by the hotel was $84.00.
(2) The total number of hand towels and bath towels purchased by the hotel was 32.
Deconstructing the QuestionLet \(h\) be the number of hand towels ($6 each).
Let \(b\) be the number of bath towels ($11 each).
We need to find the total cost.
Target Question: What is the value of \(6h + 11b\)?
***
Analyze Statement (1)"The total cost of the hand towels ... was $84.00."
This gives us the equation:
\(6h = 84\)
\(h = 14\)
We found \(h\), but we have zero information about \(b\) (the number of bath towels). The total cost \(6(14) + 11b\) cannot be determined because \(b\) is unknown.
INSUFFICIENT***
Analyze Statement (2)"The total number of hand towels and bath towels ... was 32."
This gives us the equation:
\(h + b = 32\)
We need to find \(6h + 11b\).
Since the price per item is different ($6 vs $11), knowing only the total count is not enough.
Example Case A: \(h=32, b=0 \implies Cost = 32 \times 6 = 192\)
Example Case B: \(h=0, b=32 \implies Cost = 32 \times 11 = 352\)
Different results are possible.
INSUFFICIENT***
Combine Statements (1) and (2)From Statement (1), we know \(h = 14\).
From Statement (2), we know \(h + b = 32\).
Substitute \(h = 14\) into the second equation:
\(14 + b = 32\)
\(b = 18\)
Now we have specific values for both variables (\(h=14, b=18\)). We can calculate the unique total cost:
\(Cost = 6(14) + 11(18)\)
(We do not need to perform the actual calculation; knowing that a unique value exists is enough).
SUFFICIENTAnswer: C