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11 Sep 2008, 03:49
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Difficulty:

95% (hard)

Question Stats:

53% (02:28) correct 47% (04:14) wrong based on 260 sessions

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The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is$5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?

(A) $4.50 (B)$5.10
(C) $5.30 (D)$5.50
(E) $5.60 [Reveal] Spoiler: OA Intern Joined: 12 Aug 2008 Posts: 8 Re: Zumit PS 010 [#permalink] ### Show Tags 11 Sep 2008, 10:16 3 This post received KUDOS 1 This post was BOOKMARKED dancinggeometry wrote: The price of a bushel of corn is currently$3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? (A)$4.50
(B) $5.10 (C)$5.30
(D) $5.50 (E)$5.60

Lets y be the number of days until prices are equal.

The end price of corn = 3.2 + 5xy
The end price of wheat = 5.8 - x(1.4-1) = 5.8 - 0.4xy

The two end prices are equal -> 3.2 +5xy = 5.8 - 0.4xy
From here we get that 5.4xy = 2.6, or y = 2.6/5.4x or 26/54x

Replace y in first equation and you get 3.2 + 5x(26/54x), cross the x and you get approximately 3.2 + 2.4 = $5.6 Check price for 2nd equation = 5.8 - 0.4x(26/54X), cros x and you get 5.8 - 0.2 =$5.6

I got to y = 2.6/5.4X via a number of simple methods and it took me 4-5 mins to realize this is all I needed:))
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Posts: 44290
Re: The price of a bushel of corn is currently $3.20, and the [#permalink] ### Show Tags 19 Nov 2013, 03:11 6 This post received KUDOS Expert's post 5 This post was BOOKMARKED dancinggeometry wrote: The price of a bushel of corn is currently$3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of $$5x$$ cents per day while the price of wheat is decreasing at a constant rate of $$\sqrt{2}*x-x$$ cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? (A)$4.50
(B) $5.10 (C)$5.30
(D) $5.50 (E)$5.60

Note that we are not asked in how many days prices will cost the same.

Let $$y$$ be the # of days when these two bushels will have the same price.

First let's simplify the formula given for the rate of decrease of the price of wheat: $$\sqrt{2}*x-x=1.41x-x=0.41x$$, this means that the price of wheat decreases by $$0.41x$$ cents per day, in $$y$$ days it'll decrease by $$0.41xy$$ cents;

As price of corn increases $$5x$$ cents per day, in $$y$$ days it'll will increase by $$5xy$$ cents;

Set the equation: $$320+5xy=580-0.41xy$$, solve for $$xy$$ --> $$xy=48$$;

The cost of a bushel of corn in $$y$$ days (the # of days when these two bushels will have the same price) will be $$320+5xy=320+5*48=560$$ or $5.6. Answer: E. _________________ Intern Joined: 03 Mar 2014 Posts: 8 Re: The price of a bushel of corn is currently$3.20, and the [#permalink]

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30 Apr 2014, 03:09
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I Tried using Time/Rate approach:-

Initial Price Difference = 5.80 - 3.20 = 2.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x

Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
2.6 = T(5.4x) -> T= (2.6)/5.4X

Final Price = 3.20 + 5X * T -> 3.20 + 5*2.6/5.4 = 5.6

+1 Kudos if you Like
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19 Mar 2015, 05:49
1
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Expert's post
Bunnel,

320+5xy=580-0.41xy, solve for xy --> xy=48; (Especially the last step 260/5.41)

AM

320 + 5xy = 580 - 0.41xy;

5xy + 0.41xy = 580 - 320;

5.41xy = 260

541/100*xy = 260

xy = 260*100/541 = ~48.
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Posts: 16
Location: United States
WE: Information Technology (Computer Software)

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06 Mar 2018, 10:58
dancinggeometry wrote:
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is$5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?

(A) $4.50 (B)$5.10
(C) $5.30 (D)$5.50
(E) $5.60 hi Bunuel, niks18 i have no idea if approached the question correctly, but I got correct answer 9i decoded this info x(2^1/2) - x as 2^1/2 = $$\sqrt{2}$$ = 1.4 hence x(2^1/2) - x = 1.4x -1.4 here is it please advice if it is correct solution. $$3,20 + 1.6x = 5.80 -1.4x -1.4$$ $$1.6x + 1.4x = 5.80 - 3.20-1.4$$ $$3x = 1.2$$ $$x = 2.5$$ $$3.20+2.50 = 5.70$$ so i chose $$E$$ Board of Directors Status: Stepping into my 10 years long dream Joined: 18 Jul 2015 Posts: 3228 The price of a bushel of corn is currently$3.20, and the [#permalink]

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06 Mar 2018, 11:07
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dave13 wrote:
hi Bunuel, niks18

i have no idea if approached the question correctly, but I got correct answer 9i decoded this info x(2^1/2) - x as 2^1/2 = $$\sqrt{2}$$ = 1.4 hence x(2^1/2) - x = 1.4x -1.4

$$3,20 + 1.6x = 5.80 -1.4x -1.4$$

$$1.6x + 1.4x = 5.80 - 3.20-1.4$$

$$3x = 1.2$$

$$x = 2.5$$

$$3.20+2.50 = 5.70$$

so i chose $$E$$

Hey dave13 ,

I think you did something wrong here.

Look at the highlighted text above.

How can you get \sqrt{2}x - x = 1.4x - 1.4 ? It should be 1.4x - x

Please do the question again. Try to convert dollars to cents (make same units first) and then approach.

All the best
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