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 = 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