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\begin{cases} m+p=23 \\\newline m-7=p \end{cases}\newlineThe given system of equations relates mm, the number of shirts Mara owns, and pp, the number of shirts Phil owns. \newlineWhich of the following is the best interpretation of the number 77 in the system?\newlineChoose 11 answer:\newline(A) Mara owns 77 more shirts than Phil does.\newline(B) Phil owns 77 more shirts than Mara does.\newline(C) Mara owns 77 shirts.\newline(D) Phil owns 77 shirts.

Full solution

Q. \begin{cases} m+p=23 \\\newline m-7=p \end{cases}\newlineThe given system of equations relates mm, the number of shirts Mara owns, and pp, the number of shirts Phil owns. \newlineWhich of the following is the best interpretation of the number 77 in the system?\newlineChoose 11 answer:\newline(A) Mara owns 77 more shirts than Phil does.\newline(B) Phil owns 77 more shirts than Mara does.\newline(C) Mara owns 77 shirts.\newline(D) Phil owns 77 shirts.
  1. Analyze Equation 11: Analyze the first equation in the system.\newlineThe first equation is m+p=23m + p = 23, which tells us that the total number of shirts owned by Mara (mm) and Phil (pp) together is 2323.
  2. Analyze Equation 22: Analyze the second equation in the system.\newlineThe second equation is m7=pm - 7 = p, which can be interpreted as Mara owning 77 more shirts than Phil. This is because if we add 77 to Phil's number of shirts (pp), we get Mara's number of shirts (mm).
  3. Match Interpretation: Match the interpretation of the number 77 with the given choices.\newlineBased on the second equation, we can see that the number 77 represents the difference in the number of shirts owned by Mara and Phil, with Mara owning 77 more shirts than Phil. This matches choice (A).