1. ## Find Divisor

A number when divided by a divisor leaves a remainder of 16. When twice the original number is divided by the same divisor, the remainder is 7. What would the divisor be?

My set up:

Let n = original number

Let d = divisor

n/d = 16

2n/d = 7

We have two equations in 2 unknowns.

Correct?

2. ## Re: Find Divisor

when $\displaystyle n$ is divided by $\displaystyle d$ and leaves a remainder of $\displaystyle r$

the equation for this is

$\displaystyle n=dq+r$

where $\displaystyle q$ is the quotient

so your first equation is of the form

$\displaystyle n=dq+16$

3. ## Re: Find Divisor

Originally Posted by Idea
when $\displaystyle n$ is divided by $\displaystyle d$ and leaves a remainder of $\displaystyle r$

the equation for this is

$\displaystyle n=dq+r$

where $\displaystyle q$ is the quotient

so your first equation is of the form

$\displaystyle n=dq+16$
Is the second equation 2n = dq + 7?

4. ## Re: Find Divisor

the second equation

$2n=d s+7$

the two quotients are not identical

5. ## Re: Find Divisor

\begin{align}
n &= 16 \pmod{d} \\
\implies 2n &= 32 \pmod{d} &(1)\\[8pt]
\text{also} \quad 2n &= 7 \pmod{d} &(2) \\[12pt]
(Actually it implies that $d$ divides 25, but since we know - or assume - that $16 < d < 32$ we get the result).