SOLUTION: the sum of the digits of a two digit numeral is 8. The number with the digits interchanged is 7 times the tens digit of the original number. find the original number (let u repres

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Question 71114: the sum of the digits of a two digit numeral is 8. The number with the digits interchanged is 7 times the tens digit of the original number. find the original number
(let u represent the units and t represent the tens digit. You need to solve two simultaneous equations for this one)
I honestly have no clue how to even start this one..
Found 2 solutions by checkley75, stanbon:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
U+T=8 U=8-T
T+10U=7*T NOW SUBSTITUTE (8-T) FOR U IN THIS EQUATION & SOLVE FOR T
T+10(8-T)=7T
T+80-10T-7T=0
-16T=-80
T=8-/16
T=5 THIS IS THE TENS DIGIT THEREFORE THE U NITS DIGIT IS 8-5=3
PROOF
5+10*3=7*5
5=30=35
35=35

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
the sum of the digits of a two digit numeral is 8. The number with the digits interchanged is 7 times the tens digit of the original number. find the original number
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COMMENT: Just like 23 means 10*2+3 , tu means 10*t+u
and ut means 10^u+t
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EQUATIONS:
1st: u+t = 8
2nd: 10u+t = 7t
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Solve 1st for t: t=8-u
Substitute into 2nd as follows:
10u+8-u = 7*(8-u)
9u+8 = 56-7u
16u = 48
u = 3
Then t=8-u=5
ORIGINAL NUMBER: 85
Cheers,
Stan H.