SOLUTION: 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 digi

Algebra ->  Test -> SOLUTION: 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 digi      Log On


   

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
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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."
%28%2810x%2By-7%29%29%2F%28%2810y%2Bx%29%29 = 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."
%28%2810x%2By-6%29%29%2F%28x%2By%29 = 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%2F38 = 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%2F11 = 7 with a remainder of 6