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A citrus fruit grower receives $15 for each crate of oranges

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A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post Updated on: 20 Oct 2017, 10:51
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A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

why cant we substitute the eq from a in to 15.(20+2G)+18G= , find g, substitute in O and get solution from (a) alone?

Originally posted by ekshyam on 25 Jan 2012, 03:42.
Last edited by Bunuel on 20 Oct 2017, 10:51, edited 2 times in total.
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 25 Jan 2012, 03:49
A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let \(x\) be the # of oranges and \(y\) the # of grapefruits. Note that \(x\) and \(y\) must be an integers. Q: \(x=?\)

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> \(x=2y+20\). Not sufficient to calculate \(x\)

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> \(15x+18y=38700\) --> \(5x+6y=12900\). Multiple values are possible, for istance: \(x=180\) and \(y=2000\) OR \(x=60\) and \(y=2100\).

(1)+(2) Two unknowns, two different linear equations --> We can calculate unique value of \(x\). Sufficient.

Answer: C.
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 25 Jan 2012, 03:55
thanks Bunuel :)
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 25 Jan 2012, 03:57
Hi,

If you substitute O=20+2G in the equation 15O+18G you will not be able to equate G to anything as the equation does not equal to anything

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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 25 Jan 2012, 04:28
x and Y should be intigers :P
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 27 Jan 2012, 03:23
X & Y are oranges & apples, thus should be whole numbers only.
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 26 Oct 2017, 08:34
ekshyam wrote:
A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

why cant we substitute the eq from a in to 15.(20+2G)+18G= , find g, substitute in O and get solution from (a) alone?


there is a problem here.
there is another question, in which only b is enough to solve the problem
from 2
15x + 18y = 3870

y=( 3870-15x )/18

=2150-15x/18

x must divided by 18. there are many value of x to satisfy this point. NOT SUFFICIENT

however, some problem in which there is only 1 value of x to satify, this problem normally go with small value so that we can see there is only one value of x to satisfy the problem.

becarefull to so this analysis above before you choose C.
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 26 Oct 2017, 10:25
1
each crate of oranges = $15; each crate of grapefruit = $18;
Suppose, Number of orange crates = x; Number of orange crates = y;

(1) number of crates oranges crates was 20 more than twice the number of grapefruit crates:

i.e. x= 2y + 20
No other info provided. Insuff.

(2) total income from the crates of oranges and grapefruit shipped = $38,700:

i.e. 15x + 18y = 38700
=> 5x + 6y = 12900
Multiple values of x and y are possible for the above equation. Hence, Insuff.

(1) & (2) together:
5x + 6y = 12900
substituting x's value:
5(2y + 20) +6y = 12900
=>16y = 12800 => y = 800. Sufficient.

Ans: C.
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 29 May 2018, 11:56
I am absolutely confused by this. Statement 1 alone appears to be sufficient to me. The question implies 2 equations: 15x = Gross Revenue in one week from oranges and 18g = Gross Revenue in one week from grapefruit. So, embedded in the question is a system of equations.

Then, from Statement 1 we learn that x = 2g + 20. Well, 15x = Revenue. So, I can solve for x in terms of g, right? Thus, 15 (2g + 20) = R; Thus, 30g + 300 = R. g = 10, g being the number of grapefruit.

I can put that number back into the equation denoting the relationship given in Statement 1 which was x = 2g + 20. Thus, x = 2(10) = 20; x = 40. There are 40 crates of oranges that were shipped last week.

Statement 1 alone is sufficient. How am I wrong, please tell me?




Bunuel wrote:
A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let \(x\) be the # of oranges and \(y\) the # of grapefruits. Note that \(x\) and \(y\) must be an integers. Q: \(x=?\)

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> \(x=2y+20\). Not sufficient to calculate \(x\)

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> \(15x+18y=38700\) --> \(5x+6y=12900\). Multiple values are possible, for istance: \(x=180\) and \(y=2000\) OR \(x=60\) and \(y=2100\).

(1)+(2) Two unknowns, two different linear equations --> We can calculate unique value of \(x\). Sufficient.

Answer: C.
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Re: A citrus fruit grower receives $15 for each crate of oranges  [#permalink]

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New post 29 May 2018, 12:20
I am absolutely confused by this. Statement 1 alone appears to be sufficient to me. The question implies 2 equations: 15x = Gross Revenue in one week from oranges and 18g = Gross Revenue in one week from grapefruit. So, embedded in the question is a system of equations.

Then, from Statement 1 we learn that x = 2g + 20. Well, 15x = Revenue. So, I can solve for x in terms of g, right? Thus, 15 (2g + 20) = R; Thus, 30g + 300 = R. g = 10, g being the number of grapefruit.

I can put that number back into the equation denoting the relationship given in Statement 1 which was x = 2g + 20. Thus, x = 2(10) = 20; x = 40. There are 40 crates of oranges that were shipped last week.

Statement 1 alone is sufficient. How am I wrong, please tell me?

saswata4s
saswata4s wrote:
each crate of oranges = $15; each crate of grapefruit = $18;
Suppose, Number of orange crates = x; Number of orange crates = y;

(1) number of crates oranges crates was 20 more than twice the number of grapefruit crates:

i.e. x= 2y + 20
No other info provided. Insuff.

(2) total income from the crates of oranges and grapefruit shipped = $38,700:

i.e. 15x + 18y = 38700
=> 5x + 6y = 12900
Multiple values of x and y are possible for the above equation. Hence, Insuff.

(1) & (2) together:
5x + 6y = 12900
substituting x's value:
5(2y + 20) +6y = 12900
=>16y = 12800 => y = 800. Sufficient.

Ans: C.
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Re: A citrus fruit grower receives $15 for each crate of oranges &nbs [#permalink] 29 May 2018, 12:20
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