Question 607897
The two digits a & b
10a + b = "the number"
:
"six times the sum of the digits of a two digit number is one less than the number"
6(a + b) = 10a + b - 1
6a + 6b = 10a + b - 1
6b - b = 10a - 6a - 1
5b = 4a - 1
-4a + 5b = -1
:
"and eight more than the number obtained by reversing the digits of the two digit number."
6(a + b) = 10b + a + 8
6a + 6b = 10b + a + 8
6a - a + 6b - 10b = 8
5a - 4b = 8
:
multiply the 1st equation by 5, the 2nd equation by 4:
-20a + 25b = -5
+20a - 16b = 32
-----------------adding eliminates a, find b
0 + 9b = 27
b = 27/9
b = 3
:
Find a
5a - 4b = 8
Replace b with 3
5a - 12 = 8
5a = 8 + 12
5a = 20
a = 4
:
43 is the number, the product of the digits is 12