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

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) (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."
= 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."
= 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."
= 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."
= 7 with a remainder of 6
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