To find the value of x, we need to solve the equation:

103 ÷ x = 25 remainder 3

First, let's find the total number of times x goes into 103 to get the whole number part of the quotient:

103 ÷ 25 = 4

Next, we need to find the remaining amount after dividing 103 by 25 four times:

25 x 4 = 100
103 - 100 = 3

So, the value of x is 4 with a remainder of 3.