SOLUTION: The units digit of a two digit number is 5 more than the tens digit. If the digits are reversed the new number is devided by the original the qoutient us 2 and the remainder is 7.

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Question 915250: The units digit of a two digit number is 5 more than the tens digit. If the digits are reversed the new number is devided by the original the qoutient us 2 and the remainder is 7. What is the original number?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The units digit of a two digit number is 5 more than the tens digit. If the digits are reversed and the new number is divided by the original, the qoutient is 2 and the remainder is 7. What is the original number?
***
let u=units digit
let t=tens digit
u=t+5
original number=10t+u
new number=10u+t
%2810u%2Bt%29%2F%2810t%2Bu%29=2%2B%287%2F%2810t%2Bu%29%29
%2810%28t%2B5%29%2Bt%29%2F%2810t%2Bt%2B5%29=2%2B%287%2F%2810t%2Bt%2B5%29%29
%2810t%2B50%2Bt%29%2F%2810t%2Bt%2B5%29=2%2B%287%2F%2810t%2Bt%2B5%29%29
%2811t%2B50%29%2F%2811t%2B5%29=2%2B%287%2F%2811t%2B5%29%29
%2811t%2B50%29%2F%2811t%2B5%29=%2822t%2B17%29%2F%2811t%2B5%29%29
(11t+5)(22t+17)=(11t+50)(11t+5)
242t^2+297t+85=121t^2+605t+250
121t^2-308t-165=0
solve for t by quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=121, b=-308, c=165
ans:
t=-55/121≈-0.4545(reject)
or
t=3
u=t+5=8
Check:
original number=38
new number=83
new number/original number=83/38=2+Remainder=7