A hawker stall in Toa Payoh records its daily earnings to the nearest cent. At the end of the day, the owner notices: - When the earnings are rounded to the nearest dollar, the result is $47. - When the earnings are rounded to the nearest ten cents, the result is $46.90. How many possible values could the exact daily earnings have?
Show Worked Solution
Worked Solution
Step 1: Find the range of values that round to $47 (nearest dollar).
Values that round to $47 satisfy: $46.50 <= earnings < $47.50
Call this Range A.
Step 2: Find the range of values that round to $46.90 (nearest ten cents).
Values that round to $46.90 satisfy: $46.85 <= earnings < $46.95
Call this Range B.
Step 3: The exact earnings must satisfy BOTH conditions simultaneously.
Intersection of A and B: $46.85 <= earnings < $46.95
(Range B is fully contained within Range A, so the intersection is Range B.)
Step 4: Count all possible values recorded to the nearest cent (2 decimal places).
$46.85, $46.86, $46.87, $46.88, $46.89,
$46.90, $46.91, $46.92, $46.93, $46.94
Total: 10 values
Answer: 10
Correct answer: 10
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