Question

A positive integer 'x' on division by 7 leaves remainder 5. Find the remainder when 4x +31 is divided
by 14.
​

Answer 1

Answer:

answer is r=9 when,4x+31/14

Answer 2

The remainder when 4x + 3 is divided by 14 is 9

Solution:

Given that a positive integer x on division by 7 leaves remainder 5

We know that,

$Dividend = Divisor \times quotient + remainder$

Therefore,

x = 7k + 5

Find the remainder when 4x +31 is divided  by 14

4x + 31 = 4(7k + 5) + 31

4x + 31 = 28k + 20 + 31

4x + 31 = 28k + 51 ------ eqn 1

We need to find the remainder when 4x + 31 is divided  by 14

From eqn 1,

When 28 is divided by 14, remainder is 0

When 51 is divided by 14, remainder is 9

Thus, the remainder when 4x +31 is divided  by 14 is 9

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