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# To fill a larger concert hall, a madrigal singing group consisting of

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Re: To fill a larger concert hall, a madrigal singing group consisting of [#permalink]
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Bunuel wrote:
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

Solution:

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.

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Re: To fill a larger concert hall, a madrigal singing group consisting of [#permalink]
To fill the concert hall at least 40 singers are needed. Since the singers consist of only sopranos, altos and basses, the total number of singers should be multiple of 15: 5x+7x+3x=15x
Since the smallest multiple of 15 larger than 40 is 45, then the smallest possible value of the number of singers needed is 45. The least number of basses needed is 45/5*3=9 B)
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Re: To fill a larger concert hall, a madrigal singing group consisting of [#permalink]
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Bunuel - The question needs rewording. It should be "atleast" 40 singers. Otherwise framing the inequality is not possible and the correct answer becomes A.
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Re: To fill a larger concert hall, a madrigal singing group consisting of [#permalink]
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Re: To fill a larger concert hall, a madrigal singing group consisting of [#permalink]
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