Question

what is the smallest positive integer that has a remainder of 4 when divided by 5 and a remainder of 6 when dividied by 7?
@Mathematics

Answer 1

lets call your number 'x'. then you just need to solve this:\[x=5a+4\]\[x=7b+6\]to find the smallest 'a' and 'b'

Answer 2

how do i solve this

Answer 3

since both equations have 'x' on the left-hand-side, you can equate their right-hand-sides:\[5a+4=7b+6\]\[5a=7b+2\]now what is the smallest value you can try for 'b'?

Answer 4

if you try b=1, then you would get 5a=7+2=9.
this will not give you a whole number for 'a'.
so keep increasing 'b' until you get a whole number answer for 'a'.
do you understand?

Answer 5

no i did not get it.

Answer 6

ok, we ended up with:\[5a=7b+2\]we now try increasing values for 'b' until we get a whole number solution for 'a':\[b=1, 5a=7*1+2=7+2=9\]\[b=2,5a=7*2+2=14+2=16\]\[b=3,5a=7*3+2=21+2=23\]\[b=4,5a=7*4+2=28+2=30\]30 is divisible by 5 so we know:\[5a=30\]\[a=6\]so our solution is a=6, b=4.
plug either of these into the equations we had above for 'x' to get:\[x=5a+4=30+4=34\]
so answer is 34.

Answer 7

do you understand it now?

Answer 8

yea thanx a lot

Answer 9

yw