BECE Mathematics 2011 Paper

Concept:This is a linear equation involving fractions. Multiply both sides by the LCM of the denominators to eliminate the fractions.Explanation:Start with the equation:$$\frac{1}{5}(2+y)=\frac{1}{2}(y-1)$$The denominators are $5$ and $2$. Their LCM is $10$.Multiply both sides of the equation by $10$:$$10 \times \frac{1}{5}(2+y)=10 \times \frac{1}{2}(y-1)$$This simplifies to:$$2(2+y)=5(y-1)$$Expand both sides:$$4+2y=5y-5$$Bring the variable terms to one side and the constants to the other side:$$4+5=5y-2y$$$$9=3y$$Divide both sides by $3$:$$\frac{9}{3}=y$$$$y=3$$Answer:The solution is $y=3$, which corresponds to option D.