Question

. find x and y.
12
(5) If x
405 and y

Answer 1

SolutionWe have: 9 x HATBOX = 4 x BOXHATset "HAT" =x and "BOX"=y(x,y has 3-digit)the equation becomes9(1000x+y) = 4(1000y+x) or 8996x = 3991y which on division by 13 becomes 692x = 307y where the coefficients are relatively prime. This has the obvious solution we can set as: x = 307n, y = 692n for any integer n The only solution in which x and y are both 3-digit numbers is for n = 1. Then HAT = 307 BOX = 692 9(HATBOX) = 9(307692) = 2769228 4(BOXHAT) = 4(692307) = 2769228 Thus: H=3,A=0,T=7,B=6,O=9,X=2