Problem: Find a possible value of p if the reminder when 4p is divided by 9 is 5.



Solution:

Step 1: Understanding the problem

We need to find a positive integer p such that when 4p is divided by 9, the remainder is 5.

Step 2: Using the concept of remainders

We know that if a number n is divided by d, then the remainder r is such that 0 <= r="">< d.="" />

In this case, we are given that the remainder when 4p is divided by 9 is 5.

This means that 4p can be written as 9q + 5, where q is some integer.

Simplifying this equation, we get:

4p = 9q + 5



Step 3: Finding a possible value of p

We need to find a positive integer p that satisfies the above equation.

We can use trial and error method to find a possible value of p.

Let's start by assuming q = 1.







Since p has to be a positive integer, this value of p is not valid.

Let's try with q = 2.







Again, this value of p is not valid as p has to be a positive integer.

Let's try with q = 3.







This value of p satisfies the given condition as the remainder when 4p is divided by 9 is 5.

Step 4: Conclusion

Therefore, a possible value of p is 8.

Final Answer: 8.

Since remainder is 5 then 4p-5 /9 should be divisible soo by using trial and error 4*8 = 32 -5 = 27 is divisble by 9 so p =8