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

$\dfrac x{11}=y+\dfrac4{11}\iff x=11y+4$
$\dfrac{2x}8=3y+\dfrac28\iff2x=24y+2$

$\implies 2x-x=(24y+2)-(11y+4)$
$\implies x=13y-2$
$\implies 13y-x=2$