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.
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 = 172k 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 20190115 13:00:37 