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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