Final answer:
To solve the problem, we work backwards using algebra. By dividing 47 by 3 and subtracting 19, we find the original number thought of is -3.
Step-by-step explanation:
The student's problem requires us to think of a number, add nineteen to it, and then triple the result. Given that the final answer is 47, we have to work backwards to find the initial number. The mathematics involved is simple algebra, which can often require a different type of thinking to solve, just as we might approach complicated multiplication by breaking it down into simpler components as suggested by Daniel Kahneman's example.
Let's denote the number we're thinking of as 'x'. The problem states:
- Start with x.
- Add 19 to x, which gives us x + 19.
- Triple the result, leading to 3(x + 19).
- The final result is 47, so 3(x + 19) = 47.
To find x, we first divide both sides by 3 to get x + 19 = 47 / 3. Simplifying, we find x + 19 = 15.67. Since we're likely dealing with whole numbers, triple 15 to get 45, which suggests that we should have added 2 to get 47. Therefore, our number plus 19 is 16, so x = 16 - 19. Hence, x = -3.
So, the number we thought of is -3.