The sum of two numbers is 44 , and the larger number is 2 more than the smaller number. What is the smaller number? If \( \mathrm{S}= \) the smaller number and L = the larger number, then which of the following systems of equations represents the word problem? S \( \mathrm{S}+\mathrm{L}=44 \) and \( \mathrm{L}=2 \mathrm{~S} \) S \( \mathrm{L}=44 \) and \( \mathrm{S}=\mathrm{L}+2 \) \( \mathrm{~S}+\mathrm{L}=44 \) and \( \mathrm{L}=\mathrm{S}+2 \)

To solve the problem, we need to extract the known conditions and set up the correct system of equations. 1. **Known Conditions:** - The sum of two numbers (the smaller number \( S \) and the larger number \( L \)) is 44. - The larger number \( L \) is 2 more than the smaller number \( S \). 2. **Setting Up the Equations:** - From the first condition, we can write the equation: \[ S + L = 44 \] - From the second condition, we can express \( L \) in terms of \( S \): \[ L = S + 2 \] 3. **Identifying the Correct System of Equations:** - The correct system of equations based on the conditions is: \[ S + L = 44 \quad \text{and} \quad L = S + 2 \] Now, let's check the options provided: - **Option 1:** \( S + L = 44 \) and \( L = 2S \) (Incorrect) - **Option 2:** \( L = 44 \) and \( S = L + 2 \) (Incorrect) - **Option 3:** \( S + L = 44 \) and \( L = S + 2 \) (Correct) Thus, the correct system of equations is: \[ S + L = 44 \quad \text{and} \quad L = S + 2 \] 4. **Solving the System of Equations:** Now, let's solve the system of equations to find the smaller number \( S \). Substituting \( L = S + 2 \) into the first equation: \[ S + (S + 2) = 44 \] This simplifies to: \[ 2S + 2 = 44 \] Subtracting 2 from both sides: \[ 2S = 42 \] Dividing by 2: \[ S = 21 \] Now, substituting \( S = 21 \) back to find \( L \): \[ L = S + 2 = 21 + 2 = 23 \] 5. **Final Answer:** The smaller number \( S \) is \( 21 \).