Final answer:
Upon solving the algebraic equation based on Danni's actions with the number she thought of, we find that the correct number is 8. This solution, however, does not match any of the provided multiple-choice options, indicating a possible error in the problem statement or the options given.
Step-by-step explanation:
To solve the problem where Danni thinks of a number, subtracts 2 from it, then multiplies by 8, and states that it is the same as subtracting 5 from the number and then multiplying by 16, we can set up an algebraic equation:
Let's call the number Danni is thinking of x. Following the problem statement, we have two equivalent expressions:
Setting these two expressions equal to each other gives us:
(x - 2) * 8 = (x - 5) * 16
Expanding both sides and then simplifying the equation:
8x - 16 = 16x - 80
Moving all variables to one side, we get:
8x - 16x = -80 + 16
Which simplifies to:
-8x = -64
Dividing both sides by -8 gives us:
x = 8
However, this solution is not listed in the multiple-choice options provided, so we must have made an error in our calculation. Let's try again:
Starting with (x - 2) * 8 = (x - 5) * 16, we get:
8x - 16 = 16x - 80
Bringing '16x' and '16' to the opposite sides, we get:
8x - 16x = -80 + 16
-8x = -64
x = 8
It turns out the initial solution was correct, and none of the provided options match. Therefore, either the given options are incorrect, or there may have been a mistake in the original problem statement that led to the discrepancy. In any case, based on the algebraic work, the number Danni thought of should be 8, which means the solution must be option e) The number is 8, which wasn't initially provided.