Question

Find the least whole number N greater than 40 for which:

( I ) N divided by 4 leaves a remainder of I. and
(2) N divided by 5 leaves a remainder of 3.

PLS HELP

Answer 1

*Below*

Explanation:

Let the number be N.

N divided by 4 leaves 1 as the remainder. This means N - 1 is divisible by 4.

So, we can write N - 1 = 4k1, where k1 is an integer 10 or greater

N divided by 5 leaves 3 as the remainder. This means N - 3 is divisible by 5.

So, we can write N - 3 = 5k2, where k2 is an integer 8 or greater

From above, we get 4k1 - 2 = 5k2

4k1 - 5k2 = 2

k1 = 13, k2 = 10 and the number is XXXXX = 4k1 + 1 = 4(13) + 1 = 53