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A dance troupe has a total of 50 dancers split into 2 groups.

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by BTGModeratorVI » Thu Aug 27, 2020 12:10 pm

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Difficulty—

A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

(A) $1,840
(B) $2,070
(C) $2,135
(D) $2,160
(E) $2,430

Answer: E
Source: Official guide
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Re: A dance troupe has a total of 50 dancers split into 2 groups.

by dg1900 » Fri Aug 28, 2020 2:01 am
A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

Let A be the number of costumes worn by Group A
Let B be the number of costumes worn by Group B

Using the first statement that a dance troupe has a total of 50 dancers split into 2 groups:
A + B = 50 (Eq1)
Therfore, A = 50 - B (Eq2)

Using the second statements, the costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. If the total cost of all the costumes is $4,270:
80A + 90B = 4270 (Eq3)

Substituting the value of A in Eq2 into Eq3 we get
80(50-B) + 90B = 4270
4000 - 80B + 90B = 4270
10B = 270
Therefore,
B = 27

We need total cost of the costumes worn by Group B, that is 90B, which is:
27*90= 2430
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Re: A dance troupe has a total of 50 dancers split into 2 groups.

by Brent@GMATPrepNow » Sat Aug 29, 2020 5:54 am
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:10 pm
 A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

(A) $1,840
(B) $2,070
(C) $2,135
(D) $2,160
(E) $2,430

Answer: E
Source: Official guide
We can solve this using either one variable or two variables.
Let's use one variable.

Since the question asks "What is the total cost of the costumes worn by Group B?," let's let x = the total number of dancers in Group B

A dance troupe has a total of 50 dancers split into 2 groups
If x = the number of dancers in GROUP B
Then 50 - x = the number of dancers in GROUP A

The costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. The total cost of all the costumes is $4,270
Cost = (price her costume)(number of dancers)
So, we can write: ($80)(50 - x) + ($90)(x) = $4270
Expand to get: 4000 - 80x + 90x = 4270
Simplify: 4000 + 10x = 4270
So, 10x = 270
Solve: x = 27
So, there are 27 dancers in Group B
If each costume costs $90, then the cost of those costumes = ($90)(27) = $2430

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: A dance troupe has a total of 50 dancers split into 2 groups.

by gentvenus » Sat Aug 29, 2020 10:12 am
$90 * 27 = $2430

Answer: C
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Re: A dance troupe has a total of 50 dancers split into 2 groups.

by Scott@TargetTestPrep » Wed Sep 02, 2020 5:30 am
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:10 pm
 A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

(A) $1,840
(B) $2,070
(C) $2,135
(D) $2,160
(E) $2,430

Answer: E
Source: Official guide
Solution:

We can create the equation:

A + B = 50

and

80A + 90B = 4270

Multiplying the first equation by 90, we have:

90A + 90B = 4500

Subtracting the second equation from this new equation, we have:

10A = 230

A = 23

Therefore, group B has 50 - 23 = 27 dancers. Since each of their costumes costs $90, the total cost of the costumes worn by Group B is 27 x 90 = $2430.

Answer: E

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