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?
A. 8
B. 9
C. 10
D. 11
E. 12
OA B
Source: Princeton Review
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To fill a larger concert hall, a madrigal singing group consisting of sopranos, altos, and basses, in a 5:7:3 ratio,
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BTGmoderatorDC
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Solution:BTGmoderatorDC wrote: ↑Thu Nov 12, 2020 11:10 pmTo 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?
A. 8
B. 9
C. 10
D. 11
E. 12
OA B
If we let the number of sopranos, altos, and basses be 5x, 7x and 3x, respectively, we can create the inequality:
5x + 7x + 3x ≥ 40
15x ≥ 40
x ≥ 40/15 = 8/3 = 2 ⅔
Since x must be a whole number, x is at least 3. Therefore, the number of basses is at least 3(3) = 9.
Answer: B
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