Question

When positive integer x is divided by 11, the quotient is y and the remainder is 4. when 2x is divided by 8, the quotient is 3y and the remainder is 2. what is the value of 13y – x ?

Answer 1

`\frac x{11}=y+\frac4{11}\iff x=11y+4`

`\frac{2x}8=3y+\frac28\iff2x=24y+2`


`\implies 2x-x=(24y+2)-(11y+4)`

`\implies x=13y-2`

`\implies 13y-x=2`