Each time the same letter appears it represents the same digit.Different letters represent different digits.C+C=D;D+E=17;A+2C=D;2B+C=8.Find the sum A+B+C+D+E
we have 2C=D, so
A+D=D
A=0
D+E=17
4B+D=16
17-E=4B
so, we have
(E,B)=(1,4)
(E,B)=(5,3)
(E,B)=(9,2)
that leaves us
(A,B,C,D,E) = (0,4,0,0,1) nope
(A,B,C,D,E) = (0,3,2,4,5) nope
(A,B,C,D,E) = (0,2,4,8,9) ok
so, A+B+C+D+E=23
To solve this problem, let's assign each letter a unique digit.
Let's assign the digit A to the letter A, B to the letter B, C to the letter C, and D to the letter D, and E to the letter E.
Given the equations:
C + C = D
D + E = 17
A + 2C = D
2B + C = 8
Let's substitute the values assigned to the letters into the equations.
1. C + C = D
Since the same letter represents the same digit, we can rewrite this as:
2C = D
2. D + E = 17
Substituting the value of D from equation 1:
2C + E = 17
3. A + 2C = D
Substituting the value of D from equation 1:
A + 2C = 2C
4. 2B + C = 8
Now we have a system of equations to solve:
2C = D (equation 1)
2C + E = 17 (equation 2)
A + 2C = 2C (equation 3)
2B + C = 8 (equation 4)
From equation 3, A must be 0 since A + 2C = 2C.
From equation 4, B must be 4 since 2B + C = 8, and C can't be equal to 0 according to the given information.
Now let's substitute these values into the remaining equations:
A = 0
B = 4
From equation 3, we have:
0 + 2C = 2C
0 = 0
Now let's find the value of C from equation 1:
2C = D
Since C cannot be 0, we can assign the value of 1 to C.
Thus, D = 2(1) = 2.
Substituting the values of C and D into equation 2, we have:
2(1) + E = 17
2 + E = 17
E = 17 - 2
E = 15
Finally, we can calculate the sum A + B + C + D + E:
A + B + C + D + E = 0 + 4 + 1 + 2 + 15 = 22
The sum of A + B + C + D + E is 22.
To solve this problem, we can assign variables to the unknowns. Let's assign the variables as follows:
- C represents the digit of the repeating letter.
- D represents the digit of the sum of the repeating letter.
- E represents the other digit in the sum D+E.
- A represents the other digit in the sum A+2C.
Now, let's use the provided equations to find the values of these variables:
1. C + C = D
Since the same letter represents the same digit, we can rewrite this equation as:
2C = D
2. D + E = 17
3. A + 2C = D
According to this equation, when we substitute 2C for D (from equation 1), we get:
A + 2C = 2C
A = 0
4. 2B + C = 8
Since A = 0, this equation simplifies to:
2B + C = 8
Now, let's solve these equations simultaneously:
From equation 1, we get D = 2C.
From equation 2, we have D + E = 17.
Substituting D with 2C, we get:
2C + E = 17.
From equation 4, we have 2B + C = 8.
Substituting C with D/2, we get:
2B + D/2 = 8.
Since we have D = 2C, we can rewrite the last equation as:
2B + 2C/2 = 8,
2B + C = 8.
Now, we have the system of equations:
2C + E = 17,
2B + C = 8.
Solving this system of equations using any method you prefer (substitution, elimination, etc.), we find:
C = 3,
B = 1, and
E = 11.
From equation 1, we know D = 2C, so D = 2 * 3 = 6.
Finally, to find the sum A + B + C + D + E:
A = 0,
B = 1,
C = 3,
D = 6,
E = 11.
The sum is:
0 + 1 + 3 + 6 + 11 = 21.