In the multiplication at the right,A,B,C represent different non-zero digits. each time the same letter appears it presents the same digit. Find the 2 numbers represnted by AA and BC.(0is zero). A A
x B C
------
B B O
A A
-------
6 6 0
To find the values represented by AA and BC, we will use the basic rules of multiplication and addition.
Let's analyze the multiplication:
A A
x B C
--------
B B O
A A
--------
6 6 0
From the units column, we can conclude that the product of A and C (AC) ends with 0. Since C represents a non-zero digit, the only way for the product AC to end in 0 is if A is equal to 0.
0 A
x B C
--------
B B O
0 0
--------
6 6 0
Now let's analyze the tens column. The product of A and B, plus the carry from the units column, must sum up to B. Since A is 0, the product of A and B is 0. So, the carry from the units column is B, and when added to the product of A and B, it must give B. Therefore, B must be 1.
0 1
x 1 C
--------
1 1 O
0 0
--------
6 6 0
Now we can analyze the hundreds column. The product of A and C, plus the carry from the tens column, must sum up to O (0). Since A is 0, the product of A and C is 0. Therefore, the carry from the tens column is also 0.
0 1
x 1 0
--------
1 1 O
0 0
--------
6 6 0
Now we can conclude that AA is 10 and BC is 10.
Therefore, AA = 10 and BC = 10.