6. In the multiplication problem at the right, find the sum A + B + C + D + E. Different letters represent different digits. Each time the same letter appears it represents the same digit.
E 5 2 A
x A
---------------
B 4 C D 9
A is either 3 or 7
E523
x 3
-------
(3E+1)569
E527
x 7
---------
(7E+3)689
So see which works out
To find the sum A + B + C + D + E in the multiplication problem, we can solve it step by step:
1. Start by multiplying the units digit E with the number A: E * A = 9.
2. The result of the units digit multiplication is 9, so write down 9 in the units digit position of the answer.
3. Next, multiply the tens digit C with the number A: C * A = D. This means that C multiplied by A gives a result with the tens digit D.
4. Write down the tens digit D in the tens digit position of the answer.
5. Now, multiply the hundreds digit 4 with the number A: 4 * A = C. This means that 4 multiplied by A gives a result with the hundreds digit C.
6. Write down the hundreds digit C in the hundreds digit position of the answer.
7. Next, multiply the thousands digit B with the number A: B * A = 5. This means that B multiplied by A gives a result with the thousands digit 5.
8. Write down the thousands digit 5 in the thousands digit position of the answer.
9. Finally, we have found all the digits A, B, C, D, and E in the multiplication problem:
E 5 2 A
x A
---------------
B 4 C D 9
The sum A + B + C + D + E is therefore 5 + 9 + C + D + E.
To find the sum A + B + C + D + E in the given multiplication problem, we need to solve the problem step by step.
First, let's analyze the problem. The multiplication is represented using five different letters: E, A, B, C, and D. Our goal is to find the values of these letters that satisfy the multiplication equation.
Let's start with the units column. The digit E multiplied by A gives a digit in the units column, so E multiplied by A must give the digit 9. Since A is a single-digit number, E must be a single-digit number as well. The only single-digit number that multiplied by another single-digit number gives 9 is 9 itself. So we can conclude that E = 9.
Next, let's move to the tens column. The digit C multiplied by A gives a digit in the tens column, so C multiplied by A must give the digit 4. Since A is already determined as 9, we can conclude that C = 4.
Now, let's focus on the hundreds column. The digit D multiplied by A gives a digit in the hundreds column, so D multiplied by A must give the digit B. From the multiplication equation, we know that D multiplied by 9 is equal to B. Since B is a single-digit number, D must be a single-digit number as well. By testing different values, we can find that D = 1 and B = 9.
Finally, we can substitute all the values we found into the multiplication problem:
9529
x 9
--------------
41961
Now, we can find the sum A + B + C + D + E:
A = 9
B = 9
C = 4
D = 1
E = 9
Therefore, A + B + C + D + E = 9 + 9 + 4 + 1 + 9 = 32.