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If the farmer sells 75 of his chickens, his stock of feed [#permalink]

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25 Oct 2009, 02:41

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If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60 B. 120 C. 240 D. 275 E. 300

# of chickens - x # of days - d

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals \(xd=(x-75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals \(xd=(x+100)(d-15)\).

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60 B. 120 C. 240 D. 275 E. 300

or you can make your equations in this way: Let us say he has planned for d days for c chickens. According to the question,

the food 75 chicken consumed in d days will last 20 days if consumed by (c - 75) chickens So 75d = (c - 75)20 ..... (I)

What c chickens consumed in 15 days, 100 chickens will consume in (d - 15) days 15c = 100(d - 15) ......(II)

Couple of things here: I am assuming x=y as nowhere y is defined . Also if I solve the 3 equations, (y - 75)/k = T +20 (y + 100)/k = T - 15 y/k = T

I will get k=-5. As feed/day can not be a negative number, this clearly shows that something is wrong with this approach.

It was mentioned earlier that,

x ... number of chickens k ... 1 chicken consumption per day T ... total number of days for x chickens to live given their current number

How can you get #days by dividing (y-75) by k in equation 1? You will get a quantity that will be [# of chickens * 1 chicken consu/ day]. This is not the number of days that you equate to in (y - 75)/k = T +20. For getting number of days the desired quantity should be [some unit *( day / some unit)].

The easiest way is to take the quantity that is not changing = the total feed with the farmer. Then proceed with this information as Bunuel has shown above. From my personal experience, in word problems, whenever there is a 'constant'quantity, it is better to use that to get the other values.
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Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink]

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27 Sep 2013, 09:10

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Hello from the GMAT Club BumpBot!

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If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60 B. 120 C. 240 D. 275 E. 300

# of chickens - x # of days - d

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals \(xd=(x-75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals \(xd=(x+100)(d-15)\).

Thank you for the explanation Bunuel. However, I do not understand something here: How does multiplying the number of days (d) with the number of chickens (x) give the amount of feed the farmer has ?

Shouldn't it rather be the amount of feed the chickens consume in one d days ?

That's because the amount of feed each chicken eats a day, say z, can be reduced on both sides: \(zxd=z(x-75)(d+20)\) --> \(xd=(x-75)(d+20)\); \(zxd=z(x+100)(d-15)\) --> \(xd=(x+100)(d-15)\).

Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink]

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18 Feb 2014, 16:50

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Its quite a journey but here we go. (q-75)(t+20) and (q+100)(t-15). Now we need to equal each to qt. So we will have 20q - 75t - 75(20) on the first equation and -15q + 100t - 100(15) on the second equation. We could simplify some terms but the point is we need to find 'q' so anyways after simplifying we can multiply the first equation by 3 and we're left with 12q - 60t -75 *(4) *(4) and multiply the second by 3 to get -9q + 60t - 100 (3)*3. So then we finally get to 3q = 900, q = 300

E is the answer

If any one comes up with a fast way to do this I'll def provide some Kudos Cheers! J

Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink]

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19 Oct 2013, 05:42

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Let Number of Chickens be X

The number of days chicken will eat a fixed stock will be inversely proportional to number of chickens. Hence if number of days X chicken will eat the stock will be D = K/ X

If number of chicken is reduced by 75 then D+20 = K / (X-75) If number of chicken is increaded by 100 then D-15 = K / (X+100)

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60 B. 120 C. 240 D. 275 E. 300

# of chickens - x # of days - d

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals \(xd=(x-75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals \(xd=(x+100)(d-15)\).

Thank you for the explanation Bunuel. However, I do not understand something here: How does multiplying the number of days (d) with the number of chickens (x) give the amount of feed the farmer has ?

Shouldn't it rather be the amount of feed the chickens consume in one d days ?

I find such word problems, where we have to assume some constants/variable to solve the question (that cancel out before the final solution arrives) and ALSO infer its relationship with the variables/constants given in the word problem, quite tricky (specially WORK/RATE problems! )

It'll be very helpful if you can provide some similar questions or content (or their link) to practice.

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60 B. 120 C. 240 D. 275 E. 300

# of chickens - x # of days - d

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals \(xd=(x-75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals \(xd=(x+100)(d-15)\).

Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink]

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30 Dec 2013, 04:11

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slingfox wrote:

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60 B. 120 C. 240 D. 275 E. 300

This question is similar to work-rate questions. The key is always calculate how much work each person/machine does in 1 unit of time.

For this question, we have: number of chickens = X stock feed = T (days) It means X chickens can be fed in T days --> 1 chicken eats in 1 day = 1/(XT)

1st scenario, we sell 75 chickens, we have number of chickens = X - 75 stock feed = T + 20 (days) --> 1 chicken eats 1 day = 1/[(X-75)(T+20)] Because the amount of food each chicken eats in 1 day is the same: --> 1/XT = 1/[(X-75)(T+20)] --> XT = XT+ 20X - 75T - 1500 --> 20X - 75T - 1500 = 0

2nd scenario: we buy 100 chickens number of chickens = X + 100 stock feed = T - 15 (days) --> 1 chicken eats 1 day = 1/[(X+100)(T-15)] Because the amount of food each chicken eats in 1 day is the same: --> 1/XT = 1/[(X+100)(T-15)] --> XT = XT -15X +100T - 1500 --> 15X +100T - 1500 = 0

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Couple of things here: I am assuming x=y as nowhere y is defined . Also if I solve the 3 equations, (y - 75)/k = T +20 (y + 100)/k = T - 15 y/k = T

I will get k=-5. As feed/day can not be a negative number, this clearly shows that something is wrong with this approach.

It was mentioned earlier that,

x ... number of chickens k ... 1 chicken consumption per day T ... total number of days for x chickens to live given their current number

How can you get #days by dividing (y-75) by k in equation 1? You will get a quantity that will be [# of chickens * 1 chicken consu/ day]. This is not the number of days that you equate to in (y - 75)/k = T +20. For getting number of days the desired quantity should be [some unit *( day / some unit)].

The easiest way is to take the quantity that is not changing = the total feed with the farmer. Then proceed with this information as Bunuel has shown above. From my personal experience, in word problems, whenever there is a 'constant'quantity, it is better to use that to get the other values.

Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink]

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29 Aug 2016, 08:38

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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