Decoding Letter Values for Word Sums

The problem presents a coding system where letters correspond to their numerical position in the alphabet. We need to determine the value of 'BAT' based on this system.

Establishing the Pattern

The example $\text{Z} = 26$ confirms that each letter is assigned its position number in the alphabet (A=1, B=2, ..., Z=26).

Let's verify this pattern with the given example $\text{ACT} = 24$:

• A is the 1st letter: $\text{A} = 1$
• C is the 3rd letter: $\text{C} = 3$
• T is the 20th letter: $\text{T} = 20$

Summing these values:

$ \text{ACT} = \text{A} + \text{C} + \text{T} = 1 + 3 + 20 = 24 $

The pattern holds true: the value of a word is the sum of the positional values of its constituent letters.

Calculating the Value of BAT

Now, we apply the same pattern to find the value of 'BAT':

• B is the 2nd letter: $\text{B} = 2$
• A is the 1st letter: $\text{A} = 1$
• T is the 20th letter: $\text{T} = 20$

Summing these values:

$ \text{BAT} = \text{B} + \text{A} + \text{T} = 2 + 1 + 20 = 23 $

Therefore, 'BAT' equals 23.