Decoding the Alphabetical Value Pattern
The question requires finding the value of 'CARE' based on the given values for 'ACE' and 'AGED'. We need to determine the pattern used to assign numerical values to these words.
Let's assign numerical values to letters based on their position in the alphabet: A=1, B=2, C=3, ..., Z=26.
Analyzing the Given Examples
Example 1: ACE = 35
- A = 1
- C = 3
- E = 5
- Let's test the sum of squares: $1^2 + 3^2 + 5^2 = 1 + 9 + 25 = 35$. This matches the given value.
Example 2: AGED = 91
- A = 1
- G = 7
- E = 5
- D = 4
- Let's test the sum of squares: $1^2 + 7^2 + 5^2 + 4^2 = 1 + 49 + 25 + 16 = 91$. This also matches the given value.
The established pattern is the sum of the squares of the alphabetical positions of the letters in the word.
Calculating CARE
Now, we apply this pattern to find the value of 'CARE':
- C = 3
- A = 1
- R = 18
- E = 5
Calculate the sum of the squares:
$ \text{CARE} = 3^2 + 1^2 + 18^2 + 5^2 $ $ \text{CARE} = 9 + 1 + 324 + 25 $ $ \text{CARE} = 10 + 324 + 25 $ $ \text{CARE} = 334 + 25 $ $ \text{CARE} = 359 $Therefore, CARE = 359.
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