Question

if she gave 8 chocolates to each child and 28 chocolates. if she supposed number of children as x and total chocolate as y, then form a linear equation (a) y= 5x +28 (b) 8y = x + 20 (c) y = 8x +28 (d) y=8x-20​

Answer 1

Let there be x sweets. When distributed to 25 children, 8 sweets remained. Hence x/25 gives a remainder of 8.

When distributed among 28 students,the remainder is 22.

Equations would be: x = 25a + 8 ( where a is the quotient) and x= 28b + 22 ( where b is the quotient)

This can be written as:25a = 28b +14. This means that 25a is completely divisible by 28b+14

This can be written as:

=> 25a = 25b +3b +14

Hence 3b+14 is divisible by 25

By trial we get: 3*12+14 is divisible by 25. Hence b=12.

Substituting value of b in the 2nd equation, we get the number as 28*12+22=358.

Hence the number of sweets distributed is 358