2014 Samo, senior, round 2, Question 20

Algebra Level 4

There are 300 white boxes and n red boxes in storage. Each box contains the same number of soccer balls. The total number of soccer balls in all of the boxes is n 2 + 290 n − 2490 n^{2}+290n-2490 . Determine n.


The answer is 210.

Nico Stirling by Nico Stirling , 24, Botswana

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1 solution

Unstable Chickoy
Jun 7, 2014

say x x is the number of soccer balls in each box

( n + 300 ) ( x ) = n 2 + 290 n − 2940 (n + 300)(x) = n^2 +290n -2940

( n + 300 ) ( x ) = ( n 2 + 290 n − 3000 ) + 510 (n + 300)(x) = (n^2 +290n -3000) + 510

( n + 300 ) ( x ) = ( n + 300 ) ( n − 10 ) + 510 (n + 300)(x) = (n + 300)(n - 10) + 510

( n + 300 ) [ x − ( n − 10 ) ] = 510 (n + 300)[x - (n-10)] = 510

solutions are

( n + 300 ) = 510 (n + 300) = 510 and [ x − ( n − 10 ) ] = 510 [x - (n-10)] = 510

solving for n n

( n + 300 ) = 510 (n + 300) = 510

n = 210 n = \boxed{210}

8 Helpful 0 Interesting 0 Brilliant 0 Confused

add a comment...this solution is grossly incorrect

EKENE FRANKLIN - 3 years, 2 months ago

disgustingly incorrect

Satya Kripa - 2 years, 11 months ago

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