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

Q: Why do we multiply the whole equation by 2?

Multiplying by 2 eliminates the fraction $ \frac{x}{2} $! This makes 2x + x = 30, which is much easier to solve than working with fractions.

Q: How do I know which part should be x?

Always let x represent the larger unknown. Since the first part has more questions (the second is only half), let x = first part questions.

Q: What if I get the parts backwards in my answer?

Read the question carefully! It asks for questions in each part, so list them in order: first part, second part. Here it's 10, 5 not 5, 10.

Q: Can I solve this without using fractions?

Yes! Think of it as 3 equal groups: if the second part is half the first, then first part = 2 groups, second part = 1 group. Total = 3 groups = 15 questions, so each group = 5.

Q: How do I check my answer makes sense?

Verify two things: Total questions: 10 + 5 = 15 ✓Second is half of first: 5 = 10 ÷ 2 ✓

System of Equations with Fractional Relationships

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?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 How many questions are in each part?

00:14 Let's express the number of questions in the first part as X.

00:19 Now, express the questions in the second part as, fifteen minus X.

00:25 Let's create an equation. Total questions equal fifteen.

00:30 Now, collect like terms.

00:33 Next, we need to isolate X. Move constant terms to the other side.

00:38 Convert the mixed number to a fraction.

00:42 Change division to multiplying by the reciprocal.

00:46 Now, divide fifteen by three.

00:49 Great! We've found X. Substitute it to find questions in each part.

00:54 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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?

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.

Final Answer

5, 10

Key Points to Remember

Essential concepts to master this topic

Variable Definition: Let x be first part, second part becomes x/2
Equation Setup: Total questions: $x + \frac{x}{2} = 15$
Verification: Check that 10 + 5 = 15 and 5 = 10/2 ✓

Common Mistakes

Avoid these frequent errors

Confusing which part has more questions
Don't assume the second part has more questions = wrong variable assignment! Students often think "second" means "larger" and set up x/2 + x = 15 with x/2 as the first part. Always read carefully: the second part has HALF the questions of the first part.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do we multiply the whole equation by 2?

Multiplying by 2 eliminates the fraction $\frac{x}{2}$ ! This makes 2x + x = 30, which is much easier to solve than working with fractions.

How do I know which part should be x?

Always let x represent the larger unknown. Since the first part has more questions (the second is only half), let x = first part questions.

What if I get the parts backwards in my answer?

Read the question carefully! It asks for questions in each part, so list them in order: first part, second part. Here it's 10, 5 not 5, 10.

Can I solve this without using fractions?

Yes! Think of it as 3 equal groups: if the second part is half the first, then first part = 2 groups, second part = 1 group. Total = 3 groups = 15 questions, so each group = 5.

How do I check my answer makes sense?

Verify two things:

Total questions: 10 + 5 = 15 ✓
Second is half of first: 5 = 10 ÷ 2 ✓

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