Question: 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

Correct Answer: E
Solution and Explanation:

Approach Solution 1:
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

Approach Solution 2:
By creating 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.

Approach Solution 3:
Let x and y be the number of dancers of Group A and Group B, respectively.
x+y = 50
80x + 90y = 4270
--> 8x +9y = 427
8(50-y) + 9y = 427
400- 8y+9y = 427
y = 27
--> 27*90 = 2430

“A dance troupe has a total of 50 dancers split into 2 groups.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2022." To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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