Question 402585
When a certain two digit number is divided by the number obtained by reversing
 the digits, the quotient is 2 and the remainder is 7.
 If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6. 
Find the number
:
The two digit number: x = the 10's digit; y = the units
:
"When a certain two digit number is divided by the number obtained by reversing
 the digits, the quotient is 2 and the remainder is 7."
{{{((10x+y-7))/((10y+x))}}} = 2
10x + y - 7 = 2(10y + x)
10x + y - 7 = 20y + 2x
10x - 2x = 20y - y + 7
8x = 19y + 7
:
"If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6."
{{{((10x+y-6))/(x+y)}}} = 7
10x + y - 6 = 7(x+y)
10x + y - 6 = 7x + 7y
10x - 7x = 7y - y + 6
3x = 6y + 6
divide by 3
x = (2y + 2)
:
Substitute (2y+2) for x in the 1st simplified equation
8(2y + 2) = 19y + 7
16y + 16 = 19y + 7
16 - 7 = 19y - 16y
9 = 3y
y = 3
:
Find x
x = 2y + 2
x = 3(3) + 2
x = 8
:
83 is the original number
;
:
Check solution in the statement:
When a certain two digit number is divided by the number obtained by reversing
 the digits, the quotient is 2 and the remainder is 7."
{{{83/38}}} = 2 with remainder of 7
:
do the same with the statement:
" If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6."
{{{83/11}}} = 7 with a remainder of 6