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Discounted velos (Posted on 2019-01-15) Difficulty: 2 of 5
The bicycles and tricycles in Jack's Velosale store claim 55 wheels together.
Half of the total quantity will be sold at discounted prices, the other half - regular.

Given that there are more tricycles than bicycles determine how many of each were in the store initially.

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution Comment 1 of 1
The wheels requirement means 2b + 3t = 55 (b = number of bicycles, t = number of tricycles)

Also, t > b (given) and t+b is even (by the discounts)

The solutions of the 1st equation are b = 2+3k, t = 17-2k for k >= 0. 

When k = 3, b = t and when k > 3, b > t so the solution must have k < 3.

(b+t) = 19 + k, so if this is even, k must be odd. The only odd k in the range [0,3) is k = 1, giving the solution:

b = 5, t = 15

  Posted by Paul on 2019-01-15 13:00:37
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