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 this word problem, we can set up the equations based on the information given. We know that the sum of the two numbers (the smaller number S and the larger number L) equals 44. We also know that the larger number is 2 more than the smaller number. This gives us the system of equations: \( S + L = 44 \) and \( L = S + 2 \). Now we can substitute \( L \) in the first equation to find the smaller number! In terms of real-world applications, such problems often appear in financial contexts, like budgeting or comparing prices. For instance, if you were planning a party with a set budget (like our 44) and had to allocate it based on uneven contributions from friends, you'd set similar equations to determine how much each friend contributes. Solving them gives clarity to your budget decisions!