Question

a positive integer is 3 more than multiple of 4 and 4 more than a multiple of 5 .
what is the least integer it could be?​

Answer 1

Given:

Positive integer is 3 more than multiple of 4

4 more than a multiple of 5 .

To Find:

The Least Integer

Solution:

Let the number be = x

Since, 3 more than a multiple of 4

= x  =  4a + 3

and, 4 more than a multiple of 5

= x = 5b + 4

Equating both the euqations -

4a + 3 = 5b + 4

4a  = 5b + 1

Splitting the equation -

4a = 4b + (b + 1)

b + 1 = 4x

for least values x = 1

b + 1 = 4

b = 4 - 1

b = 3 and a = 4

Thus, the equation is satisfied for b = 3  and a =  4

Now,

x = 4a + 3

= 4 × 4 + 3

= 19

and x = 5b + 4

= 5 × 3 + 4

= 19

Answer: The least number is 19.