Solve for Two Parts: Finding Question Distribution in 15-Question Math Assessment

The mathematics assessment has two parts, the second part has half of the questions of the first part, in total there are 15 questions.

How many questions are in each part?

Video Solution

Solution Steps

00:00 How many questions in each part?

00:03 Express the number of questions in the first part using X

00:06 Express the number of questions in the second part using X

00:09 Build an appropriate equation according to the given data, sum of questions equals 15

00:12 Collect terms

00:15 Isolate X

00:23 Convert from mixed number to fraction

00:26 Write division as multiplication by reciprocal

00:29 Divide 15 by 3

00:32 This is the solution for X, substitute to find the number of questions in each part

00:36 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Define variables - Let $x$ be the number of questions in the first part.
Step 2: Express the second part in terms of the first part - The number of questions in the second part is $\frac{x}{2}$ .
Step 3: Create an equation - The total number of questions is 15, hence $x + \frac{x}{2} = 15$ .
Step 4: Solve the equation:
Multiply the entire equation by 2 to eliminate the fraction:
$2x + x = 30$
This simplifies to $3x = 30$
Divide by 3: $x = 10$ .
Step 5: Determine the questions in each part:
First part: $x = 10$
Second part: $\frac{x}{2} = \frac{10}{2} = 5$ .

Therefore, the number of questions in each part is 10 for the first part and 5 for the second part.

Thus, the correct answer is choice 4: 5, 10.