WAEC Mathematics 2014 Paper

Concept:Translate the given English statement into a linear equation in one variable and solve for the unknown number.Explanation:Let the unknown number be $x$. Three quarters of the number is $\frac{3}{4}x$. Two and a half of the number is $2\frac{1}{2}x = \frac{5}{2}x$. According to the question, their sum is $13$. So we form the equation:$$\frac{5}{2}x + \frac{3}{4}x = 13$$To eliminate the fractions, multiply each term by the least common multiple of $2$ and $4$, which is $4$:$$4\left(\frac{5}{2}x\right) + 4\left(\frac{3}{4}x\right) = 4 \times 13$$Simplify each side:$$10x + 3x = 52$$Combine like terms:$$13x = 52$$Divide both sides by $13$:$$x = \frac{52}{13}$$$$x = 4$$Answer:The required number is $4$, which matches Option A.