I need help finding the lowest postive number for the my math question?

Question

What is the least positive number that you can divide by 7 and get a remainder of 4, divide by 8 and get a remainder of 5, and divide by 9 and get a remainder or 6?

Answer 1

Hmmm.... Ok.. I can do this the hard way...

start with chart with columns for X, 7x, 7x+4, (7x+4)/8, (7x+4)/9
ignore the periods below because I am using them for spacing only:
x, 7x, 7x+4, (7x+4)/8, (7x+4)/9
1, ...7, ....11,........ 1r3,..........1r2 <-- note remainders
2,. 14, ....18, ........2r2,......... 2r0
3, .21,.... 25,........ 3r1, .........2r7 <-- note the double 2's 2r0, 2r7
4,. 28,.... 32,........ 4r0,......... 3r5...notice the pattern yet?
5...........................4r7,..........4r3 <-- note the double 4's 4r0, 4r7
6...........................6r6,..........5r1
7.............................r 5.............r 8 <-- have r5 but not r6
8.............................r 4.............r 6
9.............................r 3.............r 4
10...........................r 2.............r 2
11...........................r 1.............r 0
12...........................r 0.............r 7
13...........................r 7.............r 5
14...........................r 6.............r 3
15...........................r 5.............r 1 <-- have r5 but not r6 (up 2)
16...........................r 4.............r 8
17...........................r 3.............r 6
18 2, 4
19 1,2
20 0,0
21 7,7
22 6,5
23 5,3 <-- 5 and then 1+2=3 (15 to 23 is 8 numbers)
31 5,5
39 5,7
47 5,0
55 5,2
63 5,4
71 5,6 <-- this is the one we are looking for!!!

(71*7)+4 = 501... so let's check it

501/7 = 71r4
501/8 = 62r5
501/9 = 55r6

there ya go!! must be some easy way to do it though!

Edit: hmmm... using Maple I came up with this:
for x from 1 by 1 to 1000 do
> if x mod 7=4
> and x mod 8=5
> and x mod 9=6
> then
> print(x, x mod 7, x mod 8, x mod 9)
> fi
> od;

and it printed:
>501 4 5 6

Answer 2

Haha, go do your OWN homework. I'm go relax and chill now while you do the thinking!

Answer 3

oh, my god. you're bloody mad. that's crazy. i need to go lie down...