Question

X : 12 = c, r9
X:20= c, r 12
200←x←500, x=? Va rog

Answer 1

x : 12 = c, r9
x:20= c, r 17
200←x←500, x=? 

x =12a+9
x =20b+17 
x+3 =12a+12=12(a+1)
x+3 =20b+20 =20(b+1)

12=2²×3
20=2²×5
cmmmc=2²×3×5=60

200<x<500
x+3=60x4=240  x=237
x={237,297,357,417,477}

Answer 2

x : 12 = c  (rest 9)   =>  x=12c+9 =>  200<x<500 
                           avem: x={16*12+9=201; 17*12+9=213; ... ;40*12+9=489}

x : 20 = c  (rest 17) =>  x=20c+17=> 200<x<500
                          avem: x={10*20+17=217; 11*20+17=237; ... ; 24*20+17=497}