Solve for 17 Exam Questions: Finding Distribution Across 3 Parts

A theory exam consists of 17 questions and is divided into three parts.

The second part has 3 fewer questions than the first part and the last part has half the number of questions as the first part.

How many questions are there in each part?

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 $8, 5, 4$.