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In a group of people solicited by a charity, 30 percent contributed $

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In a group of people solicited by a charity, 30 percent contributed $  [#permalink]

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New post 02 Nov 2017, 22:10
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In a group of people solicited by a charity, 30 percent contributed $40 each, 45 percent contributed $20 each, and the rest contributed $12 each. What percentage of the total contributed came from people who gave $40?

(A) 25%
(B) 30%
(C) 40%
(D) 45%
(E) 50%

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In a group of people solicited by a charity, 30 percent contributed $  [#permalink]

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New post 02 Nov 2017, 23:03
Bunuel wrote:
In a group of people solicited by a charity, 30 percent contributed $40 each, 45 percent contributed $20 each, and the rest contributed $12 each. What percentage of the total contributed came from people who gave $40?

(A) 25%
(B) 30%
(C) 40%
(D) 45%
(E) 50%


Let the total number of people solicited by a charity be x

If 30% contributed 40$ each, their contribution will be 0.3x * 40 = 12x
Similarly, as 45% contributed 20$ each, their contribution will be 0.45x * 20 = 9x
The remainder of the people contributed 12$ each.
The contribution of the remaining 0.25x will be 0.25x * 12 = 3x

Since the total contribution is 12x+9x+3x = 24x,

the percentage of those who contributed 40$ each is \(\frac{12x}{24x}\) or 50%(Option E)
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In a group of people solicited by a charity, 30 percent contributed $  [#permalink]

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New post 03 Nov 2017, 09:04
Bunuel wrote:
In a group of people solicited by a charity, 30 percent contributed $40 each, 45 percent contributed $20 each, and the rest contributed $12 each. What percentage of the total contributed came from people who gave $40?

(A) 25%
(B) 30%
(C) 40%
(D) 45%
(E) 50%

Let the # of people = 100
30 percent = 30 persons gave $40
45 percent = 45 persons gave $20
= 75 of total 100 people
"The rest [of the people]" = 25 persons, who gave $12

Total donated:
30($40) + 45($20) + 25($12) =
($1,200 + $900 + $300) = $2,400

Percentage of the total contributed that came from people who gave $40 (the 30 people):

\(\frac{$1,200}{$2,400} * 100 = 50\) percent

Answer E
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Re: In a group of people solicited by a charity, 30 percent contributed $  [#permalink]

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New post 03 Nov 2017, 10:11
Bunuel wrote:
In a group of people solicited by a charity, 30 percent contributed $40 each, 45 percent contributed $20 each, and the rest contributed $12 each. What percentage of the total contributed came from people who gave $40?

(A) 25%
(B) 30%
(C) 40%
(D) 45%
(E) 50%


Let total population be 100

So, percentage of the total contributed came from people who gave $40 = \(\frac{30*40}{(30*40)+(45*20)+(12*25)}\)\(*100\) = \(\frac{1200}{2400}\) \(*100\) = \(50\)%

Answer will be (E)
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Re: In a group of people solicited by a charity, 30 percent contributed $  [#permalink]

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New post 06 Nov 2017, 17:00
Bunuel wrote:
In a group of people solicited by a charity, 30 percent contributed $40 each, 45 percent contributed $20 each, and the rest contributed $12 each. What percentage of the total contributed came from people who gave $40?

(A) 25%
(B) 30%
(C) 40%
(D) 45%
(E) 50%


We can create the following expression:

(0.3 x 40)/(0.3 x 40 + 0.45 x 20 + 0.25 x 12)

12/(12 + 9 + 3) = 12/24 = 1/2 = 50%

Alternate Solution:

Instead of using percentages, let’s consider the percentages as numbers of people. Thus, 30 people contributed $40 each, 45 people contributed $20 each, and 25 people contributed $12 each.

Now let’s calculate the total amount contributed:

30(40) + 45(20) + 25(12) = 2400

Those contributing $40 each made a total contribution of 30(40) = 1200. Thus, their percentage of the total will be 1200/2400 x 100%, or 50%.

Answer: E
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