Elise is learning to write and decides to keep re-writing the alphabet until she knows it. She writes it in full twice, writes half of it once, then re-writes everything she has already written. How many letters has Elise written in total?

Answer: Elise has written 130 letters in total.

Step-by-step solution

Step 1: Determine the number of letters in the alphabet

The English alphabet consists of 26 letters, from 'a' to 'z'. This is the fundamental quantity we will be working with to calculate the total letters written.

Step 2: Calculate letters written in the first two full repetitions

Elise writes the full alphabet twice. To find the total letters written in this step, we multiply the number of letters in the alphabet (26) by 2.

Step 3: Calculate letters written in half a repetition

Next, Elise writes half of the alphabet once. We calculate this by multiplying the total number of letters (26) by $\frac{1}{2}$ .

Step 4: Calculate the total letters written before the final repetition

Before the final step, Elise has written the alphabet twice in full and once halfway. We add the letters from the first two full repetitions (52) and the half repetition (13) to get the initial total.

Step 5: Calculate letters written in the final repetition

Finally, Elise re-writes everything she has already written. This means she writes the current total number of letters again, which is 65.

Step 6: Calculate the grand total of letters written

To find the grand total, we add the letters written initially (65) to the letters written in the final repetition (65). This gives us the complete count of all letters Elise has written.

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