If $A + B = 96$ and $A$ is half of $B$, then the value of $A$ will be

Concept & Logic This is a linear equation problem involving substitution. By expressing one variable in terms of the other based on the given ratio, you can solve for the unknown variable using a single-variable algebraic equation. Step-by-Step Solution * Given conditions: 1) $$ A + B = 96 $$ 2) $A$ is half of $B$, which translates to $$ A = \frac{B}{2} $$ or $$ B = 2A $$ * Substitute the value of $B$ into the first equation: $$ A + 2A = 96 $$ * Combine the like terms: $$ 3A = 96 $$ * Solve for $A$: $$ A = \frac{96}{3} $$ $$ A = 32 $$ Exam Strategy & Shortcut **Ratio Method:** Since $A$ is half of $B$, the ratio of $A:B$ is $1:2$. The total parts in the sum are $1 + 2 = 3$ parts. We are given that the sum ($3$ parts) equals $96$. The value of $1$ part (which is $A$) is simply $96 \div 3 = 32$. This avoids formal algebra and is extremely fast. Common Pitfall A frequent error is misreading "$A$ is half of $B$" and mistakenly writing $A = 2B$. This leads to the incorrect calculation $3B = 96 \Rightarrow B = 32$, and $A = 64$. Always double-check the relationship before setting up the equation. Final Answer **Therefore, the correct answer is 32.**