Aaron has punchcards for her favorite tea house and her favorite coffee shop she currently has three punches on the TV punchcard and nine punches on the coffee punchcard given her regular routine she consistently earn seven new punches per week on the T punchcard and four on the coffee punch card before too long here and will have the same number punches on each card how long will that take how many punches or Aaron have on each card

The answers to the questions are;

The duration it will take for TV and coffee punch cards to have the same number of punches is 2 weeks

In 2 weeks Aaron will have an equal number of 17 punches on each (TV and coffee) card.

Step-by-step explanation:

TV = 3 + 7·x

Coffee = 9 + 4·x

Solving for x, we have

This gives 9 - 3 = 7·x - 4·x

6 = 3·x and

x = 2

Therefore in 2 weeks the number of punches on the TV and coffer punch cards will be equal

Also the number of punches on each card at the instant equal number of punches per cards is;

Number of punches on the TV card in 2 weeks = 3 + 7·2 = 17

Number of punches on the coffee card in 2 weeks = 9 + 4·2 = 17

That is Aaron has 17 punches on each card

That is Aaron will have 17 punches on each card in 2 weeks time.