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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A dance troupe has a total of 50 dancers split into 2 groups.
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BTGModeratorVI
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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
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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We can solve this using either one variable or two variables.BTGModeratorVI wrote: ↑Thu Aug 27, 2020 12:10 pmA 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
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
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Solution:BTGModeratorVI wrote: ↑Thu Aug 27, 2020 12:10 pmA 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 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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