Problem Analysis:
The problem involves a scenario where a student, Alex, is given a task to solve a mathematical problem related to the distribution of candies among children. The task requires understanding the constraints and applying logical reasoning to determine how many candies each child should receive.
#### Key Information from the Image:
1.
Total Candies: There are 24 candies.
2.
Number of Children: There are 3 children.
3.
Constraints:
- Each child must receive at least 5 candies.
- No two children can receive the same number of candies.
- The total number of candies distributed must equal 24.
#### Objective:
Determine how many candies each child should receive under these constraints.
---
Solution Approach:
To solve this problem, we need to distribute the 24 candies among the 3 children such that:
1. Each child gets at least 5 candies.
2. No two children receive the same number of candies.
3. The sum of candies received by all three children equals 24.
#### Step 1: Assign Minimum Candies
Since each child must receive at least 5 candies, let's start by assigning the minimum required candies to each child:
- Child 1: 5 candies
- Child 2: 5 candies
- Child 3: 5 candies
This分配 gives a total of:
\[
5 + 5 + 5 = 15 \text{ candies}
\]
#### Step 2: Remaining Candies
After assigning the minimum required candies, we have:
\[
24 - 15 = 9 \text{ candies remaining}
\]
#### Step 3: Distribute Remaining Candies
We now need to distribute the remaining 9 candies among the 3 children such that no two children receive the same number of candies. Let’s denote the additional candies received by each child as \( x_1, x_2, \) and \( x_3 \), where \( x_1, x_2, \) and \( x_3 \) are distinct non-negative integers.
The total additional candies must satisfy:
\[
x_1 + x_2 + x_3 = 9
\]
Additionally, since no two children can receive the same number of candies, \( x_1, x_2, \) and \( x_3 \) must be distinct.
#### Step 4: Find Distinct Values for \( x_1, x_2, \) and \( x_3 \)
To ensure distinct values, we can try small distinct integers that add up to 9. A possible set is:
\[
x_1 = 2, \quad x_2 = 3, \quad x_3 = 4
\]
These values are distinct and satisfy:
\[
2 + 3 + 4 = 9
\]
#### Step 5: Calculate Total Candies for Each Child
Now, add the additional candies to the initial minimum allocation:
- Child 1: \( 5 + 2 = 7 \) candies
- Child 2: \( 5 + 3 = 8 \) candies
- Child 3: \( 5 + 4 = 9 \) candies
#### Step 6: Verify the Solution
- Each child receives at least 5 candies: \( 7, 8, 9 \geq 5 \) (satisfied).
- No two children receive the same number of candies: \( 7, 8, 9 \) are distinct (satisfied).
- The total number of candies distributed is:
\[
7 + 8 + 9 = 24 \text{ (satisfied)}
\]
---
Final Answer:
The number of candies each child should receive is:
Parent Tip: Review the logic above to help your child master the concept of 11th grade reading comprehension worksheet.
