The sum of the weights of $A$ and $B$ is 80 kg. Half of the weight of $A$ is equal to $\frac{5}{6}$ times the weight of $B$. Find the weight of $B$.

### Concept & Logic Translate the textual relationships into a system of linear equations. Use substitution or the ratio method to isolate and solve for the target variable. ### Step-by-Step Solution * **Given:** * $A + B = 80$ * $\frac{1}{2}A = \frac{5}{6}B$ * **Calculation:** 1. Isolate $A$ in the second equation by multiplying both sides by 2: $A = 2 \times (\frac{5}{6})B$ $A = \frac{10}{6}B = \frac{5}{3}B$ 2. Substitute this expression for $A$ into the first equation: $\frac{5}{3}B + B = 80$ 3. Find a common denominator to add the terms: $\frac{5}{3}B + \frac{3}{3}B = 80$ $\frac{8}{3}B = 80$ 4. Solve for $B$: $B = 80 \times \frac{3}{8}$ $B = 10 \times 3 = 30$ kg ### Exam Strategy & Shortcut The fastest way to solve this is using the Ratio Method. From $\frac{A}{2} = \frac{5B}{6}$, we can deduce the ratio of their weights: $\frac{A}{B} = \frac{10}{6} = \frac{5}{3}$. This means $A$ is 5 parts and $B$ is 3 parts. Total parts = $5 + 3 = 8$ parts. Total weight is 80 kg, so 1 part = $80 / 8 = 10$ kg. The weight of $B$ is 3 parts, which equals $3 \times 10 = 30$ kg. ### Common Pitfall A common trap is accidentally calculating the weight of $A$ instead of $B$ at the very end. 1 part is 10 kg, making $A$ equal to 50 kg. If 50 was an option, many would rush to select it. Always double-check which variable the question is asking for. ### Final Answer **Therefore, the correct answer is 30 kg.**