Solve the cryptarithm: C + CA = ATT Where C, A, and T represent digits, CA is a two-digit number with C as tens and A as units digit, and ATT is a three-digit number with A as hundreds digit, T as tens and units digit. What is the possible value of C?

Explanation

Given the cryptarithm:

C + CA = ATT

Where:

- C is a single digit number.

- CA is a two-digit number with C in the tens place and A in the units place.

- ATT is a three-digit number with A in hundreds, and T in tens and units.

Rewrite the equation numerically:

C + (10 × C + A) = 100 × A + 10 × T + T

Simplify:

C + 10C + A = 100A + 11T  

11C + A = 100A + 11T  

11C + A - 100A = 11T  

11C - 99A = 11T  

Divide both sides by 11:  

C - 9A = T

Since C, A, T are digits 0-9:

- C - 9A = T  

- T must be a digit 0-9  

- So, C - 9A ≥ 0 and ≤ 9

Try possible values of A from 1 to 9 (A cannot be zero, since it is the hundred's digit in ATT):

Check A = 1:  

C - 9*1 = T ⇒ C - 9 = T  

Since T ≥ 0, C ≥ 9. So C=9, then T=0.

Check if this works numerically:

Left side:  

C + CA = 9 + 91 = 100

Right side:  

ATT = 1 0 0 = 100

Matches!

So the possible value of C is 9.

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