Problem Solving

BTGModeratorVI wrote: ↑

Thu Nov 05, 2020 8:00 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 ?

(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