Whole Numbers Word problem involving the least common multiple of 2 numbers $$ \square \square \square \square \square \square \square \square $$ 3/5 Español Ms. King wrote a test. Part A had true/false questions, each worth 10 points. Part B had multiple choice questions, each worth 4 points. She made the number of points for Part A equal the number of points for Part B. It was the least number of points for which this was possible. Answer the following questions. How many questions did Part A have? $$ \square $$ questions How many questions did Part B have? $$ \square $$ questions How many points was each part worth? $$ \square $$ points Explanation Check © 2025 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center I Accessibility

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To solve the problem, we need to find the least common multiple (LCM) of the points for Part A and Part B, given the conditions of the problem.

### Known Conditions:
1. Each true/false question in Part A is worth 10 points.
2. Each multiple choice question in Part B is worth 4 points.
3. The total points for Part A equals the total points for Part B.
4. We need to find the least number of points for which this is possible.

### Step-by-Step Solution:

1. **Define Variables:**
   - Let $$ a $$ be the number of questions in Part A.
   - Let $$ b $$ be the number of questions in Part B.
   - The total points for Part A is $$ 10a $$.
   - The total points for Part B is $$ 4b $$.

2. **Set Up the Equation:**
   We need to find $$ a $$ and $$ b $$ such that:
   $$
   10a = 4b
   $$

3. **Rearranging the Equation:**
   We can rearrange this equation to find a relationship between $$ a $$ and $$ b $$:
   $$
   \frac{a}{b} = \frac{4}{10} = \frac{2}{5}
   $$
   This means that for every 2 questions in Part A, there are 5 questions in Part B.

4. **Finding the Least Common Multiple:**
   To find the least number of points for which this is possible, we can express $$ a $$ and $$ b $$ in terms of a common variable $$ k $$:
   $$
   a = 2k \quad \text{and} \quad b = 5k
   $$
   The total points for Part A and Part B can be expressed as:
   $$
   \text{Points for Part A} = 10a = 10(2k) = 20k
   $$
   $$
   \text{Points for Part B} = 4b = 4(5k) = 20k
   $$

5. **Finding the Minimum Value:**
   The smallest value for $$ k $$ that keeps $$ a $$ and $$ b $$ as whole numbers is $$ k = 1 $$:
   - For $$ k = 1 $$:
     - $$ a = 2(1) = 2 $$
     - $$ b = 5(1) = 5 $$
     - Total points for each part = $$ 20(1) = 20 $$

### Final Answers:
- How many questions did Part A have? $$ 2 $$ questions
- How many questions did Part B have? $$ 5 $$ questions
- How many points was each part worth? $$ 20 $$ points

### Summary:
- Part A has $$ 2 $$ questions.
- Part B has $$ 5 $$ questions.
- Each part is worth $$ 20 $$ points.
Part A has 2 questions, Part B has 5 questions, and each part is worth 20 points.

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