\( J o h n \) is twice as old as Mary. The sum of their ages is 52 . How old is Mary? If \( J= \) John's age and \( M= \) Mary's age, which system of equations could be used to solve the problem? \[ J=M \text { and } J+M=52 \] \( J=2 M \) and \( J M=52 \) \( J \) and \( J+M=52 \)

To solve the problem, we can set up a couple of equations based on the information provided. Since John is twice as old as Mary, we can write the equation \( J = 2M \). Additionally, given that the sum of their ages is 52, we have \( J + M = 52 \). Thus, the correct system of equations to solve for their ages is: 1. \( J = 2M \) 2. \( J + M = 52 \) Now it's time to find out how old Mary is! By substituting \( J \) from the first equation into the second, we get \( 2M + M = 52 \) or \( 3M = 52 \). Solving for \( M \), we find \( M = \frac{52}{3} \approx 17.33 \). That's right, Mary is about 17 years and 4 months old! To double-check, we can plug Mary’s age back in to find John's age. If \( M \approx 17.33 \), then \( J = 2M \approx 34.67 \). The breakdown here shows how crucial it is to have a clear set of equations to work with when solving age problems!