A home owner goes to the hardware store to purchase the letters that make up a number for a sign he is making, (e.g., F-O-U-R, N-I-N-E, etc.). When he arrives, other customers are doing the same thing. The first customer buys the letters to display ONE, and pays $40. The next customer buys the letters for the number TWO, and pays $60. The last customer buys the letters for the number ELEVEN, and pays $100. Our home owner wants to buy the letters to spell out TWELVE.

Question

A home owner goes to the hardware store to purchase the letters that make up a number for a sign he is making, (e.g., F-O-U-R, N-I-N-E, etc.). When he arrives, other customers are doing the same thing. The first customer buys the letters to display ONE, and pays $40. The next customer buys the letters for the number TWO, and pays $60. The last customer buys the letters for the number ELEVEN, and pays $100. Our home owner wants to buy the letters to spell out TWELVE.

The question is: how much does the home owner pay?

Answer 1

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Answer 2

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Answer 3

To find out how much the home owner pays for the letters to spell out TWELVE, we need to determine the pattern and pricing logic behind the cost of each number.

Let's analyze the given information:
- The first customer buys the letters for the number ONE and pays $40.
- The second customer buys the letters for the number TWO and pays $60.
- The third customer buys the letters for the number ELEVEN and pays $100.

From these examples, we can observe that the cost of the letters to spell out a number consists of two components:
1) A base price that is multiplied by the number of letters in the word.
2) An additional charge that is added based on the uniqueness or complexity of the number.

For the first customer who buys the letters for the number ONE, we can calculate the base price by dividing the total cost of $40 by the number of letters in the word "ONE," which is three. Therefore, the base price is $40 / 3 = $13.33 per letter.

For the second customer who buys the letters for the number TWO, we can use a similar approach. The total cost of $60 divided by the number of letters in the word "TWO," which is three, yields a base price of $20 per letter.

Now, let's figure out the additional charge based on uniqueness or complexity. From the given examples, we can assume that each unique letter in a word adds an extra $10 to the cost.

For the first customer, the word "ONE" has three unique letters (O, N, E), so the additional charge is 3 unique letters * $10 = $30.

For the second customer, the word "TWO" also has three unique letters (T, W, O), resulting in an additional charge of 3 unique letters * $10 = $30.

Finally, for the third customer who buys the letters for the number ELEVEN, we have "ELEVEN" consisting of six letters, two of which are unique (L, V). So, the additional charge is 2 unique letters * $10 = $20.

Now, let's calculate the total cost for the home owner to buy the letters for TWELVE:

The word "TWELVE" has six letters with two unique letters (T, L).
So, the base price for each letter would be $20 (as determined from the second customer's purchase).
Since there are no additional charges for overlapping letters between "ELEVEN" and "TWELVE," we do not need to consider any additional costs.

Therefore, the total cost for the home owner to buy the letters for TWELVE is 6 letters * $20 per letter = $120.

So, the home owner pays $120 for the letters to spell out TWELVE.