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

Question

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

Archit3110 · Answer

basses can be determined 
3* 40/15 >= 8 
IMO B 9

jfranciscocuencag · Answer

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.

Gagoosh · Answer

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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Gg153 · Answer

Bunuel  B unuel  
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?

Krunaal · Answer

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.

Ilanchezhiyan · Answer

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 · Answer

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.

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

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

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