The price of each hair clip

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

The price of each hair clip

by BTGmoderatorDC » Fri Feb 16, 2018 7:24 pm

The price of each hair clip is Â¢ 40 and the price of each hair band is Â¢ 60. Rashi selects a total of 10 clips and bands from the store, and the average (arithmetic mean) price of the 10 items is Â¢ 56. How many bands must Rashi put back so that the average price of the items that she keeps is Â¢ 52?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Can some experts show me the best way to solve this problem?

OA E

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Source: Beat The GMAT — Problem Solving | Fri Feb 16, 2018 7:24 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Feb 17, 2018 4:26 am

The problem above is the same as PS71 in the OG18.
I posted three different approaches here:
https://www.beatthegmat.com/algebra-sta ... 87565.html

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 23, 2019 10:27 am

BTGmoderatorDC wrote:The price of each hair clip is Â¢ 40 and the price of each hair band is Â¢ 60. Rashi selects a total of 10 clips and bands from the store, and the average (arithmetic mean) price of the 10 items is Â¢ 56. How many bands must Rashi put back so that the average price of the items that she keeps is Â¢ 52?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

OA E

We are given that the price of each hair clip is 40Â¢ and the price of each hair band is 60Â¢. We are also given that Rashi selects 10 clips and bands from the store, with an average price of 56Â¢.

We can let the number of hair clips = h and the number of hair bands = b, and we can create the following equations:

56 = (40h + 60b)/(h + b)

56h + 56b = 40h + 60b

16h = 4b

4h = b

and

h + b = 10

Substituting 4h for b, we have:

h + 4h = 10

5h = 10

h = 2

Since h = 2, b = 8.

Next we must determine how many bands Rashi must put back so that the average price of the items that she keeps is 52Â¢. We can let n = the number of hair bands that must be put back:

52 = [(40(2) + 60(8 - n)]/(10 - n)

52(10 - n) = 80 + 480 - 60n

520 - 52n = 560 - 60n

8n = 40

n = 5

Answer: E

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