The sum of two numbers is 95 If the larger number is increased by twice the smaller number, the result is 120 What is the larger number? If \( S= \) the smaller number and \( L= \) the larger number, then which of the following systems of equations represents the word problem? \( S+L=95 \) and \( S+2 L=120 \) \( S+L=95 \) and \( 2(S+L)=120 \) \( S+L=95 \) and \( 2 S+L=120 \)

To solve this word problem, we can represent the two numbers with the equations given. The first equation \( S + L = 95 \) correctly states that the sum of the smaller number \( S \) and the larger number \( L \) is 95. The second equation should express that when we increase the larger number \( L \) by twice the smaller number \( S \), the total equals 120. This means the correct equation is \( L + 2S = 120 \). Therefore, the correct system of equations is \( S + L = 95 \) and \( 2S + L = 120 \). To find the larger number, you can solve the system of equations! Start with \( L = 95 - S \) from the first equation and substitute it into the second equation: \( 2S + (95 - S) = 120 \). By reorganizing and combining like terms, you quickly unravel the mystery to find that \( S = 25 \). Plugging that back in, \( L = 70 \). Voila! The larger number is 70!