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Step-by-Step Solution
Step 1: Understand the problem
We are given two sets of newspaper readers: 63% read newspaper A, 76% read newspaper B, and we want to find a possible percentage x that represents readers of both newspapers.
Step 2: Apply the formula for union of two sets
The total percentage (union) of readers of at least one of the newspapers is given by
$A \cup B = A + B - A \cap B$.
Substituting the given data, we get:
$A \cup B = 63 + 76 - x = 139 - x$.
Step 3: Relate the union to the total (100%)
Because the maximum percentage of all people cannot exceed 100, we must have:
$139 - x \le 100.$
Step 4: Solve the inequality
Rearranging, we find:
$139 - x \le 100 \implies x \ge 39.$
Step 5: Ensure x does not exceed individual percentages
The intersection cannot exceed either of the individual sets’ percentages, so
$x \le 63$ (since 63% is the smaller of 63% and 76%).
Step 6: Determine the valid range for x
Combining these conditions, we get
$39 \le x \le 63.$
Step 7: Check the options
The given options are: 37, 65, 29, and 55. Out of these, the only value that lies between 39 and 63 is 55. Therefore, a possible value of x is 55.
Final Answer
The correct possible value of x from the given options is 55.
