One half of a number increased by 3 is five less than two thirds of the number. What is the number?

Explanation

To solve the problem, first translate the statement into an equation: ½n + 3 = ⅔n - 5. Simplifying this, you get n = 48. Let's verify:For Option C (48):Left side: ½(48) + 3 = 24 + 3 = 27.Right side: ⅔(48) - 5 = 32 - 5 = 27.Both sides are equal, confirming 48 is the correct answer.For the other options:Option A (58): The left side equals 32, and the right side equals 34.67. They are not equal.Option B (45): The left side equals 25.5, and the right side equals 25. They are not equal.Option D (68): The left side equals 37, and the right side equals 40.33. They are not equal.Thus, the only correct answer is 48.