1. **Problem Statement:** We have five cards, each with two three-digit numbers. Some digits are obscured by ink. We need to find the card where the sum of the digits of both numbers is the same. 2. **Approach:** For each card, calculate the sum of the visible digits and express the sum of the unknown digits as variables. Then, find which card can have equal digit sums for both numbers. 3. **Card A:** Numbers: 543 and 11[ink] - Sum digits of 543: $5 + 4 + 3 = 12$ - Sum digits of 11[ink]: $1 + 1 + x = 2 + x$ - Equation: $12 = 2 + x \Rightarrow x = 10$ - Since a digit $x$ must be between 0 and 9, $x=10$ is impossible. 4. **Card B:** Numbers: 58[ink] and 11[ink] - Sum digits of 58[ink]: $5 + 8 + x = 13 + x$ - Sum digits of 11[ink]: $1 + 1 + y = 2 + y$ - Equation: $13 + x = 2 + y \Rightarrow y = 11 + x$ - Both $x$ and $y$ are digits (0 to 9), so $y = 11 + x$ cannot be less than or equal to 9. No solution. 5. **Card C:** Numbers: 982 and 1[ink][ink] - Sum digits of 982: $9 + 8 + 2 = 19$ - Sum digits of 1[ink][ink]: $1 + x + y = 1 + x + y$ - Equation: $19 = 1 + x + y \Rightarrow x + y = 18$ - Since $x$ and $y$ are digits (0 to 9), max sum is $9 + 9 = 18$, so $x=9$, $y=9$ is possible. 6. **Card D:** Numbers: 211 and 6[ink][ink] - Sum digits of 211: $2 + 1 + 1 = 4$ - Sum digits of 6[ink][ink]: $6 + x + y = 6 + x + y$ - Equation: $4 = 6 + x + y \Rightarrow x + y = -2$ - Sum of digits cannot be negative. No solution. 7. **Card E:** Numbers: 777 and 2[ink][ink] - Sum digits of 777: $7 + 7 + 7 = 21$ - Sum digits of 2[ink][ink]: $2 + x + y = 2 + x + y$ - Equation: $21 = 2 + x + y \Rightarrow x + y = 19$ - Max sum of two digits is 18, so no solution. **Final answer:** Card C is the only card where the sum of digits of both numbers can be equal. $$\boxed{\text{Card C}}$$