An integer is 1 less than twice that of another. If their sum is 23 then the smaller integer is :

Options

A. 5
B. 7
C. 11
D. 13

Answer

To solve the problem step-by-step, we can follow these instructions:

### Step 1: Define the Variables
Let the two integers be \( x \) and \( y \). According to the problem, we can assume:
- \( y \) is the integer that is one less than twice the other integer \( x \).

### Step 2: Set Up the Equations
From the problem statement, we can derive two equations:
1. \( y = 2x - 1 \) (since \( y \) is one less than twice \( x \))
2. \( x + y = 23 \) (since the sum of the two integers is 23)

### Step 3: Substitute the First Equation into the Second
Now, we can substitute the expression for \( y \) from the first equation into the second equation:
\[ x + (2x - 1) = 23 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ x + 2x - 1 = 23 \]
\[ 3x - 1 = 23 \]

### Step 5: Solve for \( x \)
Add 1 to both sides:
\[ 3x = 23 + 1 \]
\[ 3x = 24 \]
Now, divide both sides by 3:
\[ x = \frac{24}{3} = 8 \]

### Step 6: Find \( y \)
Now that we have \( x \), we can find \( y \) using the first equation:
\[ y = 2x - 1 = 2(8) - 1 = 16 - 1 = 15 \]

### Step 7: Identify the Smaller Integer
We have found \( x = 8 \) and \( y = 15 \). The smaller integer is:
\[ \text{Smaller integer} = x = 8 \]

### Final Answer
The smaller integer is **8**.

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