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Brendan has punch cards for his favorite tea house and his favorite coffee shop. He currently has 66 punches on the tea punch card and 22 punches on the coffee punch card. Given his regular routine, he consistently earns 11 new punch per week on the tea punch card and 33 on the coffee punch card. Before too long, Brendan will have the same number of punches on each card. How long will that take?\newlineWrite a system of equations, graph them, and type the solution.\newlinelank weeks\newline

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Q. Brendan has punch cards for his favorite tea house and his favorite coffee shop. He currently has 66 punches on the tea punch card and 22 punches on the coffee punch card. Given his regular routine, he consistently earns 11 new punch per week on the tea punch card and 33 on the coffee punch card. Before too long, Brendan will have the same number of punches on each card. How long will that take?\newlineWrite a system of equations, graph them, and type the solution.\newlinelank weeks\newline
  1. Define x as weeks: Let's define x as the number of weeks. For the tea punch card, Brendan starts with 66 punches and earns 11 punch per week. The equation for the tea punch card is:\newliney=x+6 y = x + 6
  2. Tea punch card equation: For the coffee punch card, Brendan starts with 22 punches and earns 33 punches per week. The equation for the coffee punch card is:\newliney=3x+2 y = 3x + 2
  3. Coffee punch card equation: Set the two equations equal to each other to find when Brendan will have the same number of punches on both cards:\newlinex+6=3x+2 x + 6 = 3x + 2
  4. Set equations equal: Solve for x by isolating it on one side:\newlinex+6−2=3x x + 6 - 2 = 3x \newline4=2x 4 = 2x \newlinex=2 x = 2

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