After weeks, Amy will have punches on each card

Question

Amy has punch cards for her favorite tea house and her favorite coffee shop. She currently has 7 punches on the tea punch card and 11 punches on the coffee punch card. Given her regular routine, she consistently earns 5 new punches per week on the tea punch card and 1 on the coffee punch card. Before too long, Amy will have the same number of punches on each card. How long will that take? How many punches will Amy have on each card?

Answer 1

Let x be the number of weeks until the number of punches on both cards is equal.

 

Then for each new week, Amy will have 5x new punches on the tea card and x new punches on the coffee card.

 

Starting with 7 punches on the tea card and 11 punches on the coffee card, the equation below can be used to calculate when the punches are the same.

 

7 + 5x = 11 + x

 

4x = 4

 

x = 1

 

Therefore, the number of punches on both cards will be equal after 1 week.