Solve for 17 Exam Questions: Finding Distribution Across 3 Parts

To solve the problem, follow these steps:

• Define variable $x$ as the number of questions in the first part.
• Express the number of questions in the second and last parts in terms of $x$, which are $x-3$ and $\frac{x}{2}$ respectively.
• Set up the equation for the total number of questions: $x + (x - 3) + \frac{x}{2} = 17$.

Now, let's solve the equation:
Combine like terms:
$x + x - 3 + \frac{x}{2} = 17$
This simplifies to:
$2x + \frac{x}{2} - 3 = 17$.

Clear the fraction by multiplying the entire equation by 2:
$2(2x) + 2\left(\frac{x}{2}\right) - 2(3) = 2(17)$,
which simplifies to:
$4x + x - 6 = 34$.

Combine the terms:
$5x - 6 = 34$.
Add 6 to both sides:
$5x = 40$.
Divide by 5 to solve for $x$:
$x = 8$.

The number of questions in the first part is 8.

To find the number of questions in the second part, calculate $x - 3$:
$8 - 3 = 5$.

For the last part, calculate $\frac{x}{2}$:
$\frac{8}{2} = 4$.

In conclusion, there are 8 questions in the first part, 5 questions in the second part, and 4 questions in the last part.

Therefore, the solution to the problem is $8, 5, 4$.