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Bushel of Corn and Peck of wheat

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by gmatv09 » Thu Aug 20, 2009 8:17 am
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
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by real2008 » Thu Aug 20, 2009 10:38 am
is it E
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by PussInBoots » Thu Aug 20, 2009 11:35 am
3.20 + 5 * x * days = 3.2 + 5 * k
5.80 - (1.4x - x) * days = 5.80 - .4 * x * days = 5.8 - .4k

5.4k = 2.6 <=> k is close to .5

3.2 + 5 *.5 = 5.7

E
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by gmatv09 » Thu Aug 20, 2009 1:26 pm
OA E
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by tom4lax » Fri Aug 21, 2009 5:25 am
3.20 + 5 * x * days = 3.2 + 5 * k
5.80 - (1.4x - x) * days = 5.80 - .4 * x * days = 5.8 - .4k

5.4k = 2.6 <=> k is close to .5

3.2 + 5 *.5 = 5.7

E

In the above, why are you using 5 * x * days instead of .05 * x * days. Isn't it an increase of 5 cents / day?

I think the same could be said for the price of wheat... No?

I realize this gets to the correct answer however.

EDIT: I used following, gets to the same answer.

3.20 + .05x = 5.8 - .004x
.054x = 2.6
x = ~50 days
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