Denise has punch cards for her favorite tea house and her favorite coffee shop. She currently has 4 punches on the tea punch card and 5 punches on the coffee punch card. Given her regular routine, she consistently earns 4 new punches per week on the tea punch card and 3 on the coffee punch card. Before too long, Denise will have the same number of punches on each card. How long will that take? How many punches will Denise have on each card?
Call x the number of weeks it will take for both cards to have the same number of punches.....we have
5 + 3x = 4 + 4x
5 -4 = 4x - 3x
1 = x
It will take one week and each card will have 5 + 3(1) = 8 punches