SOLUTION: I am thinking of a number between 40 and 100 when the number is divided by 8 the remainder is 1 and when the number is divided by 9 the remainder is 4 what is the number

So it's 4 more than a multiple of 9.

The multiples of 9 that we can add 4 to and be between 40 and 100 are
36, 45, 54, 63, 72, 81, 90 So our number is 4 more that one of those, or

List of possibilities: 40, 49, 58, 67, 76, 84, 94

The multiples of 8 that we can add 1 to and be between 40 and 100 are
40, 48, 56, 64, 72, 80, 88, 96. So our number is 4 more that one of these,
or

List of possibilities: 41, 49, 57, 65, 73, 81, 89, 97.

49, since it's the only number in both lists.

Edwin