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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineKhalil has punch cards for his favorite tea house and his favorite coffee shop. He currently has 22 punches on the tea punch card and 55 punches on the coffee punch card. Given his regular routine, he consistently earns 55 new punches per week on the tea punch card and 22 on the coffee punch card. Before too long, Khalil will have the same number of punches on each card. How many punches will Khalil have on each card? How long will that take?\newlineKhalil will have _\_ punches on each card in _\_ weeks.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineKhalil has punch cards for his favorite tea house and his favorite coffee shop. He currently has 22 punches on the tea punch card and 55 punches on the coffee punch card. Given his regular routine, he consistently earns 55 new punches per week on the tea punch card and 22 on the coffee punch card. Before too long, Khalil will have the same number of punches on each card. How many punches will Khalil have on each card? How long will that take?\newlineKhalil will have _\_ punches on each card in _\_ weeks.
  1. Define equations for punch cards: Step 11: Define the equations for Khalil's punch cards.\newlineFor the tea punch card, Khalil starts with 22 punches and earns 55 punches per week. The equation representing the total punches on the tea card over time is:\newliney=5x+2 y = 5x + 2 \newlineFor the coffee punch card, Khalil starts with 55 punches and earns 22 punches per week. The equation representing the total punches on the coffee card over time is:\newliney=2x+5 y = 2x + 5
  2. Set equations equal to solve: Step 22: Set the equations equal to solve for x using substitution.\newline5x+2=2x+5 5x + 2 = 2x + 5 \newlineSolving for x:\newline5x−2x=5−2 5x - 2x = 5 - 2 \newline3x=3 3x = 3 \newlinex=1 x = 1
  3. Substitute x to find y: Step 33: Substitute x = 11 back into either equation to find y.\newlineUsing the tea punch card equation:\newliney=5(1)+2 y = 5(1) + 2 \newliney=7 y = 7

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