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Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math. To help her concentrate better on math, she spends 20 minutes more dancing than doing math. Part A: Write a pair of linear equations to show the relationship between the number of minutes Pam practices math every day (x) and the number of minutes she practices dances every day (y). (5 points) Part B: How much time does Pam spend on practicing math every day? (3 points) Part C: Is it possible for Pam to have spent 60 minutes practicing dance every day? Explain your reasoning. (2 points)
do part a
Let: d = minutes dancing Let: m = minutes doing math She spends 80 min doing both. d + m = 80 She dances for 20 min more than she does math d = m + 20 You now have a system of equations. Equation #2 is already in d in terms of m, so use that to substitute the expression into equation 1, then solve for the remaining variable. d + m = 80 (m + 20) + m = 80 2m = 60 m = 30 Now that we know "m", we can solve for "d" d = m + 20 d = 30 + 20 d = 50 She dances for 50 min and does math for 30.