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I think it's easier to think of this conceptually.
If we're working in the remainder system, there no such things as decimals. So if I've got 17 cookies and 4 friends, and I want to divide the cookies evenly, each friend gets 4 and the remainder is 1.
But in the decimal system, remainders are fine. So to go from the remainder system to the decimal system, I take the last cookie and cut into four parts, one for each friend. That gives me 1/4, or .25 additional cookies for everyone.
From this, I've got a useful relationship:
Remainder / Divisor = Decimal portion
Applied to our problem, we've got y friends and 9 cookies left, so
9 / y = .12
or y = 75
If we're working in the remainder system, there no such things as decimals. So if I've got 17 cookies and 4 friends, and I want to divide the cookies evenly, each friend gets 4 and the remainder is 1.
But in the decimal system, remainders are fine. So to go from the remainder system to the decimal system, I take the last cookie and cut into four parts, one for each friend. That gives me 1/4, or .25 additional cookies for everyone.
From this, I've got a useful relationship:
Remainder / Divisor = Decimal portion
Applied to our problem, we've got y friends and 9 cookies left, so
9 / y = .12
or y = 75
