Final answer:
To solve for three consecutive numbers where 9 times the first equals the third plus 7 times the second, an equation is formed and solved. Upon finding the solution (9, 10, 11) which was not in the options, and testing the given choices, none of the options match the condition, implying an error in the question or the options.
Step-by-step explanation:
The student is asked to find three consecutive numbers such that 9 times the first number equals the third number plus 7 times the second number. Let's represent the first number as n, which makes the second number n + 1, and the third number n + 2. The equation based on the problem's condition is:
9n = (n + 2) + 7(n + 1)
Solving this equation:
- 9n = n + 2 + 7n + 7
- 9n = 8n + 9
- n = 9
Therefore, the three consecutive numbers are 9, 10, and 11.
However, this set of numbers is not one of the given options, meaning there might have been a miscalculation or that there's no correct option among the given choices. Upon revisiting our equation, if any of the given choices were correct, the set of consecutive numbers would satisfy the following condition:
9 × (First Number) = (Third Number) + 7 × (Second Number)
Testing option (c) (7, 8, 9):
- 9 × 7 = 9 + 7 × 8
- 63 = 9 + 56
- 63 = 65
Option (c) is not correct, as the equation does not equal. None of the other options will satisfy the given condition, so we can conclude that there was likely an error in the question or the provided options.