Problem Analysis:
The problem involves understanding and solving a system of linear equations. The task is to determine the values of two integers, \( x \) and \( y \), based on the given conditions.
#### Given Conditions:
1.
Sum of Two Integers: The sum of two integers is 24.
\[
x + y = 24
\]
2.
Difference of Two Integers: One integer is twice as large as the other.
\[
x = 2y \quad \text{(or equivalently, } y = 2x\text{)}
\]
#### Objective:
Find the values of \( x \) and \( y \) that satisfy both conditions.
---
Step-by-Step Solution:
#### Step 1: Represent the Conditions Mathematically
From the problem, we have two equations:
1. \( x + y = 24 \)
2. \( x = 2y \)
#### Step 2: Substitute the Second Equation into the First
Using the second equation \( x = 2y \), substitute \( x \) in the first equation:
\[
x + y = 24
\]
\[
2y + y = 24
\]
#### Step 3: Simplify the Equation
Combine like terms:
\[
3y = 24
\]
#### Step 4: Solve for \( y \)
Divide both sides by 3:
\[
y = \frac{24}{3} = 8
\]
#### Step 5: Solve for \( x \)
Now that we have \( y = 8 \), substitute this value back into the equation \( x = 2y \):
\[
x = 2y = 2 \cdot 8 = 16
\]
#### Step 6: Verify the Solution
Check if the values \( x = 16 \) and \( y = 8 \) satisfy both original conditions:
1.
Sum Condition: \( x + y = 16 + 8 = 24 \) (satisfied)
2.
Difference Condition: \( x = 2y \Rightarrow 16 = 2 \cdot 8 \) (satisfied)
Both conditions are satisfied, so the solution is correct.
---
Final Answer:
\[
\boxed{x = 16, y = 8}
\]
Parent Tip: Review the logic above to help your child master the concept of consecutive integer problems worksheet.
