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To fill a larger concert hall, a madrigal singing group consisting of 27 Feb 2019, 23:09
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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, needs 40 singers. What is the least number of basses the group will need?

A. 3
B. 6
C. 9
D. 12
E. 15
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To fill a larger concert hall, a madrigal singing group consisting of 28 Feb 2019, 03:33
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Bunuel
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. 3
B. 6
C. 9
D. 12
E. 15
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basses can be determined
3* 40/15 >= 8
IMO B 9
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To fill a larger concert hall, a madrigal singing group consisting of 30 Jun 2019, 18:40
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Can someone please give another approach?

If Basses are 9 means that:

3x = 9

x = 3

And then 15x will be 45, which is more than the singers required.

Please help.
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To fill a larger concert hall, a madrigal singing group consisting of 30 Jun 2019, 19:27
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jfranciscocuencag
Can someone please give another approach?

If Basses are 9 means that:

3x = 9

x = 3

And then 15x will be 45, which is more than the singers required.

Please help.
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Equate 15x with 40;

15x=40
X=8/3

Since x cannot be a decimal and must be a whole number and a multiple of 3, the least possible number is 9.

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To fill a larger concert hall, a madrigal singing group consisting of 14 Jun 2025, 10:15
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Bunuel Bunuel
Wouldn't the group need 3k=(40*3)/15 = 8 basses? if there are 9 basses than the total number of singers will shift to 45?
Bunuel
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. 3
B. 6
C. 9
D. 12
E. 15
Show more
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To fill a larger concert hall, a madrigal singing group consisting of 14 Jun 2025, 11:18
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sanya511
Bunuel Bunuel
Wouldn't the group need 3k=(40*3)/15 = 8 basses? if there are 9 basses than the total number of singers will shift to 45?
Bunuel
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. 3
B. 6
C. 9
D. 12
E. 15
Show more
The basses have to be a multiple of 3, because sopranos and altos need to be integers, if you consider basses to be 8 then sopranos and altos will become decimals - which is not possible. Therefore, we need at least 9 basses. There's no constraint if singers are more than 40, but we need at least 40. Hope it helps.
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To fill a larger concert hall, a madrigal singing group consisting of 31 Jul 2025, 02:26
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If basses have to be multiple of 3, why does the question suggest that Bass =3/15(40) = 8; Does that not make Bass= 8? I am confused. Could you please explain?
Krunaal
sanya511
Bunuel Bunuel
Wouldn't the group need 3k=(40*3)/15 = 8 basses? if there are 9 basses than the total number of singers will shift to 45?
Bunuel
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. 3
B. 6
C. 9
D. 12
E. 15
The basses have to be a multiple of 3, because sopranos and altos need to be integers, if you consider basses to be 8 then sopranos and altos will become decimals - which is not possible. Therefore, we need at least 9 basses. There's no constraint if singers are more than 40, but we need at least 40. Hope it helps.
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To fill a larger concert hall, a madrigal singing group consisting of 31 Jul 2025, 02:58
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Ilanchezhiyan
If basses have to be multiple of 3, why does the question suggest that Bass =3/15(40) = 8; Does that not make Bass= 8? I am confused. Could you please explain?
Krunaal
The basses have to be a multiple of 3, because sopranos and altos need to be integers, if you consider basses to be 8 then sopranos and altos will become decimals - which is not possible. Therefore, we need at least 9 basses. There's no constraint if singers are more than 40, but we need at least 40. Hope it helps.
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We are told that concert needs 40 singers, i.e. we need at least 40 singers; and these singers should be in the ratio 5:7:3 => Total singers = \(5x + 7x + 3x = 15x\)

Now, if you take 15x = 40, x = 40/15 => you will get bases = 8, but what about sopranos and altos? 7*(40/15), and 5*(40/15) => these are decimals, and singers can't be counted as decimals. So, while it is told that the hall needs 40 singers, you cannot have exactly 40 singers, it will be more than 40.

Therefore, when you take total no. of singers as 45, i.e. 15x =45, x = 3 => you get all proper values of all singers i.e. 15, 21, and 9. Thus, you'll have minimum a total of 45 singers, which includes 9 bases. Hope it helps.
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