If a, b, and c are digits for which
7 a 2
-4 8 b
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To find the value of a, b, and c in the given equation:
7 a 2
-4 8 b
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We need to look at the addition of the last two digits in the vertical addition. In this case, the last digit is "2" plus "b". Since the addition results in a single digit, we know that b must be equal to 6.
Now, let's proceed to the addition of the first column. We have "7" plus "-4", which should give us a single digit number. However, since the given sum is positive, we know there must be a carry from the multiplication of the second column with the "-4".
This indicates that the sum of the multiplication of -4 with "8" and "-4" with "a" is greater than 10. The only way this is possible is if a is equal to 2, which means -4 * 8 = -32. Therefore, the carry value is equal to 3.
So, now we can complete the addition:
7 2
- 4 8
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3 0 2
Therefore, the values of a, b, and c in the equation are a = 2, b = 6, and c = 0.