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In a farm, the ratio of pigs to chickens is 13 to 28. When

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In a farm, the ratio of pigs to chickens is 13 to 28. When [#permalink] New post 28 Oct 2012, 22:01
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In a farm, the ratio of pigs to chickens is 13 to 28. When 15 pigs were added to the farm, the ratio of pigs to chickens became 4 to 7. What was the original total number of pigs and chickens in the farm?

(A) 200
(B) 205
(C) 210
(D) 215
(E) 220

[Reveal] Spoiler:
I suppose that, [13][/28] + 15 pigs can be [16][/28] to reduce the fraction we probably will receive [4][/7],
so 3 in numrator is equal - 15 pigs
the total number of pigs before new comers = 13*5=75

how can I get the number of chickens?

Thanx

Last edited by actleader on 29 Oct 2012, 21:54, edited 2 times in total.
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Re: Arithmetic In a farm, the ratio of pigs to chickens is 13 to [#permalink] New post 28 Oct 2012, 22:11
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actleader wrote:
Hi! Could you help me with tne next problem solving question.

In a farm, the ratio of pigs to chickens is 13 to 28. When 15 pigs were added to the farm, the ratio of pigs to chickens became 4 to 7. What was the original total number of pigs and chickens in the farm?

I suppose that, [13][/28] + 15 pigs can be [16][/28] to reduce the fraction we probably will receive [4][/7],
so 3 in numrator is equal - 15 pigs
the total number of pigs before new comers = 13*5=75

how can I get the number of chickens?

Thanx


Pigs:Chicken = 13:28
No of pigs = 13x, No of chicken = 28x

When 15 more pigs were added, ratio becomes 4:7 i.e.

\(\frac{(13x+15)}{28x} = \frac{4}{7}\)
x = 5

Initially, the no of pigs was 13x = 13*5 = 65
No of chicken was 28x = 28*5 = 140
Original total = 205

or Original total = 13x + 28x = 41x = 41*5 = 205
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Re: In a farm, the ratio of pigs to chickens is 13 to 28. When [#permalink] New post 29 Oct 2012, 00:29
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actleader wrote:
In a farm, the ratio of pigs to chickens is 13 to 28. When 15 pigs were added to the farm, the ratio of pigs to chickens became 4 to 7. What was the original total number of pigs and chickens in the farm?

[Reveal] Spoiler:
I suppose that, [13][/28] + 15 pigs can be [16][/28] to reduce the fraction we probably will receive [4][/7],
so 3 in numrator is equal - 15 pigs
the total number of pigs before new comers = 13*5=75

how can I get the number of chickens?

Thanx


Similar questions to practice;
two-numbers-are-in-the-ratio-5-6-if-22-is-added-to-the-135168.html
a-physics-class-has-majors-and-non-majors-in-a-ratio-of-4-to-133685.html
the-ratio-of-two-positive-numbers-is-3-to-4-if-k-is-added-95198.html

Hope it helps.
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Re: In a farm, the ratio of pigs to chickens is 13 to 28. When [#permalink] New post 03 Nov 2012, 08:13
Bunuel wrote:
actleader wrote:
In a farm, the ratio of pigs to chickens is 13 to 28. When 15 pigs were added to the farm, the ratio of pigs to chickens became 4 to 7. What was the original total number of pigs and chickens in the farm?

[Reveal] Spoiler:
I suppose that, [13][/28] + 15 pigs can be [16][/28] to reduce the fraction we probably will receive [4][/7],
so 3 in numerator is equal - 15 pigs
the total number of pigs before new comers = 13*5=75

how can I get the number of chickens?

Thanx


Similar questions to practice;
two-numbers-are-in-the-ratio-5-6-if-22-is-added-to-the-135168.html
a-physics-class-has-majors-and-non-majors-in-a-ratio-of-4-to-133685.html
the-ratio-of-two-positive-numbers-is-3-to-4-if-k-is-added-95198.html

Hope it helps.


VeritasPrepKarishma, Bunuel
thanx for solving the problem but I'd like yo know how can I found the number of chickens when I deducted that 3 in numerator is equal - 15 pigs?
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Re: In a farm, the ratio of pigs to chickens is 13 to 28. When [#permalink] New post 03 Nov 2012, 20:53
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actleader wrote:

VeritasPrepKarishma, Bunuel
thanx for solving the problem but I'd like yo know how can I found the number of chickens when I deducted that 3 in numerator is equal - 15 pigs?


Yes, when you say that the the additional 3 is actually 15, you get 5 as the multiplier.

In your solution above, you wrote:
"the total number of pigs before new comers = 13*5=75" which should actually be "the total number of pigs before new comers = 13*5=65" (calculation error)

Next, no of chickens will be 28*5 = 140
(after all, you have already found that the multiplier of the ratio is 5. You multiplied 13 by 5 to get the number of pigs. You multiply 28 by 5 to get the number of chickens)
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Re: In a farm, the ratio of pigs to chickens is 13 to 28. When [#permalink] New post 03 Nov 2012, 21:48
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actleader wrote:
In a farm, the ratio of pigs to chickens is 13 to 28. When 15 pigs were added to the farm, the ratio of pigs to chickens became 4 to 7. What was the original total number of pigs and chickens in the farm?

(A) 200
(B) 205
(C) 210
(D) 215
(E) 220

[Reveal] Spoiler:
I suppose that, [13][/28] + 15 pigs can be [16][/28] to reduce the fraction we probably will receive [4][/7],
so 3 in numrator is equal - 15 pigs
the total number of pigs before new comers = 13*5=75

how can I get the number of chickens?

Thanx


15sec approach to solve this question:
Original ratio is 13:28, which shows the original total must be a multiple of 41. Only 205 among answer choices is multiple of 41.
Ans B it is.

Further, since you are interested in finding number of chickens too..Once you've total number, you can deduce number of chickens, pigs and everything else since you've the ratio given.
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Re: In a farm, the ratio of pigs to chickens is 13 to 28. When [#permalink] New post 30 Jan 2014, 10:58
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Re: In a farm, the ratio of pigs to chickens is 13 to 28. When   [#permalink] 30 Jan 2014, 10:58
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