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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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:))

320 + 5xy = 580 - 0.41xy;

5xy + 0.41xy = 580 - 320;

5.41xy = 260

541/100*xy = 260

xy = 260*100/541 = ~48.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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 \(E\)

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!