To fill a larger concert hall, a madrigal singing group consisting of sopranos, altos, and basses, in a 5:7:3 ratio,

[BTGmoderatorDC]

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

[Scott@TargetTestPrep]

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

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.

Answer: B