Final answer:
To solve this problem, assume the three consecutive odd integers are represented by n, n+2, and n+4. Write equations based on the given information and solve to find n and the largest integer.
Step-by-step explanation:
To solve this problem, let's assume that the three consecutive odd integers are represented by n, n+2, and n+4. The sum of the smallest integer and twice the largest integer is n + 2(n+4). The median integer is n + 2. The problem states that this sum is ten squared more than the median integer. So we can write the equation as: n + 2(n+4) = (n + 2)^2 + 10^2.
Expanding and simplifying the equation gives us: n + 2n + 8 = n^2 + 4n + 4 + 100.
Combining like terms gives us: 3n + 8 = n^2 + 4n + 104.
Bringing all terms to one side of the equation gives us: n^2 + n - 96 = 0.
Factoring the quadratic equation gives us: (n - 8)(n + 12) = 0.
So n = 12 or n = -8. Since we are dealing with odd integers, n must be 12. Therefore, the largest integer is n + 4 = 12 + 4 = 16. So the correct option is d. 69.