i am a number less than 3000. when u divide me by32, my remainder is 30. when u divide me by 58, my remainder is 44

Answer 1

x < 3000

x is a positive integer = 798, 1726 or 2654

3 solutions

if you count negative integers, then an infinite number of solutions

x/32= y + remainder of 30

798/32=24 +remainder 30

1726/32=53+ remainder 30

x/58 = z + remainder of 44

798/58= 13 remainder 44

1726/58= 29 remainder 44

x = 32y + 30

x = 58z + 44

if y =1, x =62

if y=2, x = 94

126,158,190,222,254,286,318,350,382,414,446,478,510,542,574,606,638,670.702,734,766,798,830,862,

894,926,958,990,1022,1054,1086,1118,1150,1182,1214,1246,1278,1310,1342,1374,1406,1438,1470,1502,

1534,1566,1598,1630,1662,1694,1726,1758,1790,1822,

...

if y=90, x = 2910

if y=92 x=2974

if z=1, x =102

if z=2, x = 160

218,276,334,392,450,508,566,624,682,740,798,856,914,972,1030,1088,1146,1204,1262,1320,1378,1436,1494,1552,1610,1668,1726,1774,1832

...

if z =50, x =2944

LCM= 2(15)(29)=870

870/58= 15

870/32= 58

870+58=928

798+928 = 1726

1726+928= 2654

2654/58= 45 with remainder 44

2654/32= 82 with remainder 30