## Kimberly has punch cards for her favorite tea house and her favorite coffee shop. she currently has 6 punches on the tea punch car

Question

Kimberly has punch cards for her favorite tea house and her favorite coffee shop. she currently has 6 punches on the tea punch card and 5 punches on the coffee punch card. given her routine, she consistently earns 6 new punches per week on the tea punch card and 7 on the coffee punch card. before too long, kimberly will have the same number of punches on each card. how many punches will kimberly have on each card? how long will that take?

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16 mins 2023-01-25T13:34:05+00:00 1 Answer 0 views 0

1. By arithmetic series, the cards will have the same 12 punches in one week.
From that question, we know that the initial punches on Kimberly’s card are
Initial Tea = 6
Initial Coffee = 5
For each week, Kimberly earns 6 punches for tea and 7 punches for coffee, Which means that we can use the arithmetic series for determining how much Kimberly earns punches for n-week.
Tea = 6 + 6i
Coffee = 5 + 7i
where i is the number of weeks.
The number of punches will be the same, hence we can write the equation to
Tea = Coffee
6 + 6i = 5 + 7i
7i – 6i = 6 – 5
i = 1
Hence, the cards will have the same number in one week.
Substitute the value of i to Tea
Tea = 6 + 6i
Tea = 6 + 6(1)
Tea = 12 punches
the total punches on each card are 12.
For more on arithmetic at : https://brainly.com/question/24295771
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