The problem presents a pattern where certain letters are assigned numerical values. We need to identify this pattern and then apply it to find the sum of the values of P, E, S, and T.

Letter Value Pattern

Let's carefully examine the given information to uncover the underlying rule:

• E = 10
• J = 20
• O = 30
• T = 40

We can observe that these letters (E, J, O, T) correspond to specific positions in the English alphabet:

• E is the 5^th letter.
• J is the 10^th letter.
• O is the 15^th letter.
• T is the 20^th letter.

Comparing the alphabetical position with the assigned value, we can see a clear relationship:

• For E: Alphabetical position is 5. Given value is 10. (5 × 2 = 10)
• For J: Alphabetical position is 10. Given value is 20. (10 × 2 = 20)
• For O: Alphabetical position is 15. Given value is 30. (15 × 2 = 30)
• For T: Alphabetical position is 20. Given value is 40. (20 × 2 = 40)

Therefore, the pattern is: Value = Alphabetical Position × 2.

Calculating Letter Values

Now, let's use this identified pattern to find the values of P, E, S, and T.

Summing the Values (P + E + S + T)

Finally, we need to calculate the sum of these determined values:

\( P + E + S + T = 32 + 10 + 38 + 40 \)

Let's add them step-by-step:

• 32 + 10 = 42
• 42 + 38 = 80
• 80 + 40 = 120

The total sum is 120.

Final Answer

Based on the alphabetical pattern where each letter's value is twice its position in the alphabet, the sum P + E + S + T is 120.