Question

Micheal has punch cards for his favorite tea house and his favorite coffee shop. He currently has 2 punches on the tea punch card and 6 punches on the coffee punch card. Given his regular routine, he consistently earns 6 new punches per week on the tea punch card and 2 on the coffee punch card. Before too long, Micheal will have the same of punches on each card. How long will that take?

Answer 1

The two cards will have the same number of punches in 1 week.

Step-by-step explanation

Micheal has 2 punches on his tea punch card and 6 punches on his coffee punch card.

It is also said that he earns 6 new punches per week on the tea punch card and 2 new punches per week on the coffee punch card.

We are then told to find when the two punch cards will have the same number of punches.

Let the number of weeks this will take be x.

For Tea punch card, in x weeks, there will be

(2 + 6x) punches

For Coffee punch card, in x weeks, there will be

(6 + 2x) punches

When they are equal, we will have

2 + 6x = 6 + 2x

6x - 2x = 6 - 2

4x = 4

Divide both sides by 4

(4x/4) = (4/4)

x = 1 week

Hope this Helps!!!