John is twice as old as Mary. The sum of their ages is 21 . How old is Mary? Let \( J= \) John's age and \( M= \) Mary's age. Select the system equations that represents the problem. \( J+M=21 \) \( M-2 J=0 \) \( J-2 M=0 \) \( J=M+2 \)

To find out how old Mary is, we can set up a system of equations based on the problem statement. Let's use the equations provided. We know from the problem that John is twice as old as Mary, which translates to \( J = 2M \). The sum of their ages is 21, represented by \( J + M = 21 \). Now, we can reformulate the equations as: 1. \( J + M = 21 \) 2. \( J = 2M \) Plug the second equation into the first equation to solve for M: \( 2M + M = 21 \) That simplifies to \( 3M = 21 \), leading us to find that \( M = 7 \). So, Mary is 7 years old, and John is 14! Isn’t it fun how we can use simple algebra to unravel the mystery of ages?