SOLUTION: When a two digit number is divided by the sum of its digits the quotient is8.If the ten's digit is diminished by three times the unit's digit,the remainder is 1.What is the number?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: When a two digit number is divided by the sum of its digits the quotient is8.If the ten's digit is diminished by three times the unit's digit,the remainder is 1.What is the number?      Log On


   

Question 629235: When a two digit number is divided by the sum of its digits the quotient is8.If the ten's digit is diminished by three times the unit's digit,the remainder is 1.What is the number?
Answer by lwsshak3(11628) About Me  (Show Source):
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When a two digit number is divided by the sum of its digits the quotient is8.If the ten's digit is diminished by three times the unit's digit,the remainder is 1.What is the number?
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let u=units digit
let t=tens digit
..
t-3u=1
t=3u+1
..
(10t+u)/(t+u)=8
10t+u=8t+8u
10(3u+1)+u=8(3u+1)+8u
30u+10+u=24u+8+8u
31u-32u=-10+8
u=2
t=3u+t=7
number: 72