In a class of 50 students, the ratio of boys to girls is 3 : 2. The average weight of girls is 36 kg less than that of boys. If the average weight of the whole class is 54 kg, find the average weight of boys (in kg).

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The correct answer is 68.4.

Step 1: Find the number of boys and girls in the class.
The total number of students in the class is 50, and the ratio of boys to girls is 3 : 2.
Sum of the ratio parts = 3 + 2 = 5.

$\text{Number of boys}=\frac{3}{5}\times 50=30$

$\text{Number of girls}=\frac{2}{5}\times 50=20$

Step 2: Calculate the total weight of the class.
Given that the average weight of the whole class is 54 kg:

$\text{Total weight of the class}=50\times 54=2700\text{kg}$

Step 3: Set up an equation for the average weight of boys.
Let the average weight of boys be $B$ kg.
Since the average weight of girls is 36 kg less than that of boys, the average weight of girls is $(B-36)$ kg.

$\text{Total weight of boys}=30\times B=30B$

$\text{Total weight of girls}=20\times (B-36)=20B-720$

Step 4: Solve for $B$.
The total weight of the class is the sum of the total weight of boys and girls:

$30B+20B-720=2700$

$50B$$50\mathrm{B<mo>-</mo><mn>720</mn><mo>=</mo><mn>2700</mn>}$

$50\mathrm{B<mo>=</mo><mn>2700</mn><mo>+</mo><mn>720</mn>}$

$50\mathrm{B<mo>=</mo><mn>3420</mn>}$

$\mathrm{B<mo>=</mo><mfrac><mrow><mn>3420</mn></mrow><mrow><mn>50</mn></mrow></mfrac><mo>=</mo><mn>68.4</mn><mtext>\; kg</mtext>}$

Thus, the average weight of boys is 68.4 kg.