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# A \$550 donation to a community fund is to be divided among three organ

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Math Expert
Joined: 02 Sep 2009
Posts: 58410
A \$550 donation to a community fund is to be divided among three organ  [#permalink]

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06 Feb 2019, 02:44
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:49) correct 11% (02:03) wrong based on 63 sessions

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A \$550 donation to a community fund is to be divided among three organizations. The hospital is to get twice as much as The community recreation center and three time as much as the volunteer fire company. How much of the donation is to go to the community recreation center?

A. \$50
B. \$75
C. \$100
D. \$150
E. \$200

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Posts: 1467
Concentration: Accounting, Finance
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Re: A \$550 donation to a community fund is to be divided among three organ  [#permalink]

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06 Feb 2019, 02:49
Bunuel wrote:
A \$550 donation to a community fund is to be divided among three organizations. The hospital is to get twice as much as The community recreation center and three time as much as the volunteer fire company. How much of the donation is to go to the community recreation center?

A. \$50
B. \$75
C. \$100
D. \$150
E. \$200

let community reaction center got = x

Hospital = 2x

Volunteer fire company = 2x/3.

x + 2x + 2x/3 = 550

3x + 6x + 2x = 1650

11x = 1650

x = 150.

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Joined: 28 Sep 2018
Posts: 29
A \$550 donation to a community fund is to be divided among three organ  [#permalink]

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06 Feb 2019, 02:55
1
Let Hospital be H
Let Community recreation be CR
Let Fire company be FC

Given :-
H = 2CR
H = 3FC
And \$550 = H + CR + FC

Approach

Since we are given 3 terms and 1 eqn we will equate all to one variable.

We know the relationship of H with the other two variables

Solution

550 = H + H/2 + H/3
550 = 11H/6
H = 300

Thus CR = H/2 = \$150

(D)

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Re: A \$550 donation to a community fund is to be divided among three organ  [#permalink]

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06 Feb 2019, 06:20
1
Bunuel wrote:
A \$550 donation to a community fund is to be divided among three organizations. The hospital is to get twice as much as The community recreation center and three time as much as the volunteer fire company. How much of the donation is to go to the community recreation center?

A. \$50
B. \$75
C. \$100
D. \$150
E. \$200

let community recreation get = x
hospital = 2x
fire co = 2x/3

x+2x+2x/3 = 550
x = 150
IMO D
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Joined: 29 Nov 2018
Posts: 168
Re: A \$550 donation to a community fund is to be divided among three organ  [#permalink]

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27 May 2019, 07:32
To avoid fractions,

Set hospital's ratio at 6 parts

Now,
H:C = 2:1 --- equation (1)
= 6:3

also,
H:F = 3:1 --- equation (2)
= 6:2

From (1) and (2), we get
H:C:F:total = 6:3:2:11

therefore,
C's share= (3/11) * \$550
= \$150
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Re: A \$550 donation to a community fund is to be divided among three organ  [#permalink]

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28 May 2019, 18:08
Bunuel wrote:
A \$550 donation to a community fund is to be divided among three organizations. The hospital is to get twice as much as The community recreation center and three time as much as the volunteer fire company. How much of the donation is to go to the community recreation center?

A. \$50
B. \$75
C. \$100
D. \$150
E. \$200

We can let h = the donation to the hospital, c = the donation to the community recreation center and f = the donation to the volunteer fire company. We can create the equations:

h = 2c

h/2 = c

And

h = 3f

h/3 = f

Thus:

550 = h + h/3 + h/2

Multiplying by 6, we have:

3,300 = 6h + 2h + 3h

3,300 = 11h

300 = h, so c = 150

Answr: D
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Re: A \$550 donation to a community fund is to be divided among three organ   [#permalink] 28 May 2019, 18:08
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