Question

If a natural number 'a' is divided by 7, the remainder
is 5. If a natural number 'b' is divided by 7, the
remainder is 3. The remainder is 'r' if a + b is divided
by 7. Find the value of 3r+5/4

Answer 1

Given :  a natural number 'a' is divided by 7, the remainder  is 5. If a natural number 'b' is divided by 7, the  remainder is 3. The remainder is 'r' if a + b is divided  by 7

To Find : Value of (3r+5)/4  

Solution:

'a' is divided by 7, the remainder  is 5

=> a = 7m  + 5

'b' is divided by 7, the  remainder is 3

=> b = 7n + 3

a + b = 7m + 5 + 7n + 3

=> a + b = 7m + 7n + 8

=> a + b = 7m + 7n + 7 + 1

=> a + b = 7(m + n + 1) + 1

=> a + b = 7k + 1

The remainder is 'r' if a + b is divided  by 7

=> a + b = 7k + r

=> r = 1

(3r+5)/4  

= (3*1  + 5)/4

= (3 + 5)/4

= 8/4

= 2

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