WAEC Mathematics 2010 Paper

Concept:Let the two consecutive whole numbers be $x$ and $x+1$.Use the given relation between their sum and product to form a quadratic equation.Explanation:Sum of the numbers: $x + (x+1) = 2x+1$.Product of the numbers: $x(x+1)$.Given condition: $2x+1 = \frac{5}{6}x(x+1)$.Multiply both sides by $6$: $6(2x+1) = 5x(x+1)$.So $12x+6 = 5x^2+5x$.Rearrange: $5x^2+5x-12x-6=0$.Thus $5x^2-7x-6=0$.Factorise: $5x^2-10x+3x-6=0$.$5x(x-2)+3(x-2)=0$.$(5x+3)(x-2)=0$.So $5x+3=0$ or $x-2=0$.This gives $x=-\frac{3}{5}$ or $x=2$.Since $x$ must be a whole number, reject $x=-\frac{3}{5}$.Hence $x=2$, and the next consecutive number is $x+1=3$.Answer:The required consecutive whole numbers are $2$ and $3$.