The sum of the digits is 11. 7 less than the reversed number is twice the original number. Find the REVERSED number.

Question

I am stuck on this one plz help

Answer 1

t + u = 11 the digits of a 2 digit number sum to 11

-7 +2(10u +t) = 2(10t +u). translated from "subtract 7 from twice the number which is the reverse digits of the original number"

2 equations 2 unknowns

solve by substitution, elimination, matrix algebra or graph the two equations and find their intersection point

20t +2u = 20u +2t -7 (and a 3rd restriction: u and t are both integers) 2 unknowns 3 restrictions means it's possible there is no solution. but more likely one unique solution in this problem

18t - 18u = -7 is 2nd equation after combining like terms

t + u = 11 multiply both sides by 18

18t +18u = 198

add last to 2nd to last equation

36t = 191

t = 191/36 = 5 11/36 which is Not an integer

u = 5 25/36 is also Not an integer

so seemingly No solution, DNE

unless there's a mistake(s) above somewhere?

graphing solution is (u,t) = about (10.8, 0.2) or vice versa

either way no real solution as u and t must be integers

while graphing and substitution&elimination gave different answers,

indicating at least 1 was a mistake, odds are super high there is no solution

extra credit, find a mistake above and a real integer solution and you win a free

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