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Initially, the ratio of potbellied pigs to carrots in a room had been

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Bunuel
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Initially, the ratio of potbellied pigs to carrots in a room had been [#permalink] New post   06 Feb 2020, 05:35
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Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

A. 350
B. 300
C. 358
D. 200
E. 275
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Re: Initially, the ratio of potbellied pigs to carrots in a room had been [#permalink] New post   06 Feb 2020, 06:18
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Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

A. 350
B. 300
C. 358
D. 200
E. 275

Pigs = 6, Carrots ate by pigs = x

Initially - \(\frac{P}{C} = \frac{1}{60 }\)->\(\frac{ 6}{C} = \frac{1}{60} \)-> \(C=360\)

Later - \(\frac{P}{(C-x)} = \frac{3}{1 }\)->\(\frac{ 6}{(360-x)} = 3 \)-> \(2=360-x\) -> \(x=358\) -> Answer - C
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Re: Initially, the ratio of potbellied pigs to carrots in a room had been [#permalink] New post   07 Feb 2020, 12:39
Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

We are given that original ratio of P/C = 1/60. We know that there were 6 pigs in the room.

P/C = 1/60 = 6/x.
X = 360 Carrots in the room initially.

New ratio of P/C after carrots were eaten is 1/3. From this we know the number of pigs will stay the same but the number of carrots will change.

6/(360-carrots eaten) = 3/1

Carrots eaten = 358.

Anyone have a quicker way to solve this?
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Initially, the ratio of potbellied pigs to carrots in a room had been [#permalink] New post   25 Feb 2020, 12:05
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Step 1: We are told that there were 6 pigs so, the original ratio 1:60 gets multiplied by 6 --> 6:360

Step 2: The new ratio is 3:1 but, since there were 6 bigs, multiply this ratio by 2 --> 6:2

Step 3: 360-2 = 358
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Re: Initially, the ratio of potbellied pigs to carrots in a room had been [#permalink] New post   02 Mar 2020, 06:59
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Bunuel wrote:
Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

A. 350
B. 300
C. 358
D. 200
E. 275


Since there were 6 potbellied pits in the room initially, there were 360 carrots initially. Now, we can create the equation:

6 / (360 - n) = 3/1

6 = 1080 - 3n

3n = 1,074

n = 358

Answer: C
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Re: Initially, the ratio of potbellied pigs to carrots in a room had been [#permalink]
02 Mar 2020, 06:59
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