To fill a larger concert hall, a madrigal singing group consisting of sopranos, altos, and basses, in a 5:7:3 ratio, needs 40 singers. What is the least number of basses the group will need?

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sopranos : altos : basses =

5:7:3

Requirement = 40 singers

Total Number of Basses =

\frac{3 \times 40}{5+7+3} = \frac{120}{15} = 8

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.