Discussion
The ratio of the number of boys to the number of girls in a class of 64 students is 5 : 3. If 6 more girls are added to the class, then how many more boys should be admitted so that the ratio of boys to that of the girls becomes 3 : 2 ?
Answer: C
The class needs 5 more boys.
With 64 students in the ratio 5 : 3, there are \(64 \times \frac{5}{8} = 40\) boys and 24 girls. After 6 more girls join, there are 30 girls. For the ratio of boys to girls to be 3 : 2:
\[ \text{boys} = 30 \times \frac{3}{2} = 45 \]
So \(45 - 40 = 5\) more boys must be admitted. Check: 45 : 30 = 3 : 2. 6, 8 and 12 more boys would give 46 : 30, 48 : 30 and 52 : 30, none of which is 3 : 2.
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