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11 Sep 2008, 03:49
3
13
00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:28) correct 51% (03:42) wrong based on 374 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 $$x\sqrt{2} - x$$ 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

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19 Nov 2013, 03:11
7
10
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.

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11 Sep 2008, 10:16
3
1
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:)) Intern Joined: 13 Sep 2013 Posts: 2 Re: The price of a bushel of corn is currently$3.20, and the price of a  [#permalink]

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18 Mar 2015, 05:59
Bunnel,

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

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20 Mar 2016, 01:49
1
1
I am not sure if this will be effective for all. Since the numbers are very small, direct decrease and increase of price will solve the problem quickly. But this is trail and error method. if not able to figure out in 30 seconds, should go ahead with the standard method.

Corn increase by 5x and wheat by x (2^1/2)-x which effectively is .4x

lets say x = .1, then corn increase by .5 and wheat decrease by .04

corn Wheat
day 0 3.2 5.8
day 1 3.7 5.76
day 2 4.2 5.72
day 3 4.7 5.68
day 4 5.2 5.64
day 5 5.7 5.6

So the price will match up in the range 5.6 to 5.64. Looking at options 5.6 is the answer.
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Re: The price of a bushel of corn is currently $3.20, and the price of a [#permalink] ### Show Tags 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

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

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

$$3x = 1.2$$

$$x = 2.5$$

$$3.20+2.50 = 5.70$$

so i chose $$E$$
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21 Jul 2018, 06:28
Bunuel I'm a little confused by this last line:

541/100*xy = 260

xy = 260*100/541 = ~48.

Did you just divide 26,000 by 541 in your head or something? I'm confused how people are getting that ballpark 48 number. Guess and check? Thanks!

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