H2. 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?
Solution
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
$$
\begin{aligned}
2 p+3 c+2 k & =88-75 \\
& =13,
\end{aligned}
$$
and from the second sentence we have
$$
p+c+k=6,
$$
so that
$$
2 p+2 c+2 k=12 .
$$

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.