Hamilton 2015 Q2
2. In Vegetable Village it costs 75 pence to buy 2 potatoes, 3 carrots and 2 leeks at the Outdoor Market, whereas it costs 88 pence to buy 2 potatoes, 3 carrots and 2 leeks at the Indoor Market.
To buy a potato, a carrot and a leek costs 6 pence more at the Indoor Market than it does at the Outdoor Market.
What is the difference, in pence, between the cost of buying a carrot at the Outdoor Market and the cost of buying a carrot at the Indoor Market?
Hamilton Olympiad 2015, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: 1 penny
Suppose that a potato costs \(p\) pence more at the Indoor Market than at the Outdoor Market, that a carrot costs \(c\) pence more, and that a leek costs \(k\) pence more. Note that some or all of \(p\), \(c\) and \(k\) may be negative.
Then from the first sentence we obtain
and from the second sentence we have
so that
Subtracting equation (2) from equation (1), we get \(c = 1\).
Hence the cost of buying a carrot at the Indoor Market is one penny more than buying a carrot at the Outdoor Market.
Solution © UK Mathematics Trust, from the Hamilton Olympiad 2015 solutions.