Let the number be x. The statement “three times the number decreased by 5 equals 16” translates to the equation 3x − 5 = 16. Adding 5 to both sides gives 3x = 21, and then dividing by 3 yields x = 7. Substituting back into the original relation, 3 × 7 − 5 equals 21 − 5 = 16, confirming that 7 satisfies the condition.
Option A:
Option A, 5, when substituted gives 3 × 5 − 5 = 10, which is not equal to 16. Thus, it fails to satisfy the equation implied by the verbal statement.
Option B:
Option B fits the equation exactly, turning 3x − 5 into 16 when x is 7. This closes the loop between the word problem and its algebraic representation.
Option C:
Option C, 9, would make 3 × 9 − 5 = 22, overshooting the stated result 16, so it cannot be correct.
Option D:
Option D, 11, yields 3 × 11 − 5 = 28, which is even further from 16 and clearly inconsistent.
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