messa

New member
my question is: If q and r are whole numbers such that 109=5q-r and 0<r<5, find q and r.

What I did was picked a number for r because it has to be between 1 and 4 I picked 4.

109=5q-r
109=5q-4
113=5q
q=22.6

I know that's not the right answer though because what about 1,2, and3?

soroban

Elite Member
Hello, messa!

If q and r are whole numbers such that 109 = 5q - r and 0 < r < 5, find q and r.
. . . . . . . . . . . . . . .r + 109
Solve for q: . q .= .---------
. . . . . . . . . . . . . . . . .5

Since q is a whole number, the numerator must be divisible by 5.

From a choice of r = {1,2,3,4}, the only value is: r = 1

. . . Then: q = 22

messa

New member
okay, so even if i didn't know to solve for q, i could have substituted 1-4 in for r and used the only one that gave me a whole number?

thanks a bunch