When the integer n is divided by 18, the quotient is x and the remainder is 6, When the integer n is divided by 25, the quotient is y and the remainder is 15. Which of the following is true?

The correct option is 18x − 25y = 9.

Step-by-step Explanation:

According to the division algorithm, any integer $n$ can be represented as:

$n=\text{divisor}\times \text{quotient}+\text{remainder}$

From the first statement given in the problem:

When the integer $n$ is divided by 18, the quotient is $x$ and the remainder is 6.

We can write this as Equation (1):

$n=18x+6$

From the second statement given in the problem:

When the integer $n$ is divided by 25, the quotient is $y$ and the remainder is 15.

We can write this as Equation (2):

$n=25y+15$

Since both equations represent the same integer $n$, we can equate them:

$18x+6=25y+15$

Now, rearrange the terms to group the variables on one side and the constant values on the other side:

$18x-25y=15-6$

$18x-25y=9$

Thus, the true relationship is 18x − 25y = 9.