EROM x 9 = MORE
To prevent confusion between the letter O and the digit 0 (zero),
let's change the letter O to the letter A, then when we write "0",
we will know it is a zero, and not the letter O.
ERAM * 9 = MARE
Change 9 to 10 - 1
ERAM*(10 - 1) = MARE
ERAM*10- ERAM = MARE
ERAM*10 = MARE + ERAM
When you multiply ERAM by 10 you annex a zero on the right end,
getting ERAM0, so
ERAM0 = MARE + ERAM
Write that as an addition in vertical fashion, letting x, y,
and z be the numbers to carry, which can only be 0 or 1
x y z
E R A M
+M A R E
---------
E R A M 0
E is obviously 1, since x+E+M could not possibly add to
more than 18 even if they were large as possible. So we have:
x y z
1 R A M
+M A R 1
---------
1 R A M 0
Looking at the rightmost column, M is obviously 9, with a 1
to carry, so z=1, and now we have:
x y 1
1 R A 9
+9 A R 1
---------
1 R A 9 0
x could not be a carry of 1, for that would make R=1,
but E is already 1, so R=0 (zero), and x is 0 to carry,
so now we have:
0 y 1
1 0 A 9
+9 A 0 1
---------
1 0 A 9 0
In the next to the rightmost column, A is obviously 8,
making y=0 to carry, so we have:
0 0 1
1 0 8 9
+9 8 0 1
---------
1 0 8 9 0
Now we compare that to
x y z
E R A M
+M A R E
---------
E R A M 0
E=1, R=0, A=8, M=9, x=0, y=0, z=1
So the answer to
ERAM x 9 = MARE
is
1089 x 9 = 9801
The problem only asked for the value of R, so the answer is 0 (zero),
choice B)
Edwin
