Substitute different digits (0, 1, 2..,9) for different letters in the...
Introduction:
The problem requires substituting different digits (0, 1, 2, ..., 9) for different letters in the word "MONEY", so that the corresponding addition is correct and it results in the maximum possible value of MONEY. We need to determine the maximum value of MONEY by finding suitable digits for each letter.
Solution:
To find the maximum value of MONEY, we need to assign the digits such that it forms the largest number possible. Let's analyze the given problem step by step.
Step 1: Assigning Digits for Letters
We have the word "MONEY" and we need to assign different digits to each letter. Let's assign digits from largest to smallest to maximize the value of MONEY.
- Assigning 9 to 'M': This is the largest available digit, so we assign it to 'M'.
- Assigning 8 to 'O': We assign the second largest digit, 8, to 'O'.
- Assigning 7 to 'N': We assign the third largest digit, 7, to 'N'.
- Assigning 6 to 'E': We assign the fourth largest digit, 6, to 'E'.
- Assigning 5 to 'Y': We assign the fifth largest digit, 5, to 'Y'.
Step 2: Forming the Numbers
Now that we have assigned digits to each letter, we can form the numbers based on the given equation.
- MONEY = 98765
- + 10364
- + 210563
- + 3210978
Step 3: Calculating the Sum
Now, we calculate the sum of the numbers:
- MONEY = 98765
- + 10364
- + 210563
- + 3210978
----------------------
= 3546970
Step 4: Checking the Options
The maximum possible value of MONEY is 3546970.
- Option 1: 1 (10364) + 2 (10563) + 3 (10978) + 4 (None of these) = 10364 + 10563 + 10978 + 4 = 31909
- Option 2: 3 (10978) + 5 (None of these) + 4 (None of these) + 6 (None of these) = 10978 + 0 + 0 + 0 = 10978
- Option 3: 3 (10978) + 5 (None of these) + 4 (None of these) + 7 (None of these) = 10978 + 0 + 0 + 0 = 10978
Therefore, the maximum possible value of MONEY is 3546970, which does not match any of the given options. Hence, the correct answer is "None of these."
Conclusion:
By assigning the digits 9, 8, 7, 6, and 5 to the letters of "MONEY," we can form the maximum possible value of 3546970. This value