In the addition of the 3 digit numbers shown, the letters A, B, C, D each represent a unique single digit. Which of the following could be the sum of A+B+C+D?
ABC+DBC=850
a. 10. b. 13. c.14. d.16. e.19
175+675
5+7+1+6 = 19
19
Well, when it comes to addition and math problems, I'm more of a jokester than a mathematician. But let's give it a shot!
In the equation ABC + DBC = 850, we need to find the sum of A, B, C, and D. Since A, B, C, and D represent unique single digits, the sum of A+B+C+D must be equal to 10.
So the answer is a) 10! Just like the perfect 10 I am with my jokes!
To find the possible sum of A+B+C+D, we need to solve the equation ABC + DBC = 850.
Let's break this down step by step:
1. We are given that A, B, C, and D each represent a unique single digit. This means that A, B, C, and D are all distinct from each other and can take on any digit from 0 to 9.
2. In the given equation, ABC represents a 3-digit number where A is in the hundreds place, B is in the tens place, and C is in the ones place. Similarly, DBC represents a 3-digit number where D is in the hundreds place, B is in the tens place, and C is in the ones place.
3. To solve the equation, we need to add the two 3-digit numbers, ABC and DBC, on the left-hand side to get the sum of 850 on the right-hand side.
Now, let's substitute the values and find the possible sum of A+B+C+D:
From ABC + DBC = 850, we can rewrite it as:
(100A + 10B + C) + (100D + 10B + C) = 850
Combining like terms:
100A + 10B + C + 100D + 10B + C = 850
Simplifying:
100A + 10B + C + 100D + 10B + C = 850
100A + 100D + 2C + 20B = 850
Dividing both sides by 10:
10A + 10D + C + 2B = 85
Now, we can see that the sum A + B + C + D is equal to:
(A + B + C + D) = (10A + 10D + C + 2B) - 85
Therefore, to find the possible values of the sum A + B + C + D, we need to find all possible values of (10A + 10D + C + 2B) that are greater than or equal to 85 and subtract 85 from them.
We can test the answer choices:
a. 10: (10A + 10D + C + 2B) - 85 = 10 - 85 = -75 (Not a possible sum)
b. 13: (10A + 10D + C + 2B) - 85 = 13 - 85 = -72 (Not a possible sum)
c. 14: (10A + 10D + C + 2B) - 85 = 14 - 85 = -71 (Not a possible sum)
d. 16: (10A + 10D + C + 2B) - 85 = 16 - 85 = -69 (Not a possible sum)
e. 19: (10A + 10D + C + 2B) - 85 = 19 - 85 = -66 (Not a possible sum)
Based on the calculations, none of the given answer choices could be the sum of A + B + C + D.
well, you know that C+C=0 or C+C=10
so, either C=0 or C=5
see what you can do with that...