B2. The Smith family went to a restaurant and bought two Pizzas, three Chillies and four Pastas. They paid $£ 53$ in total.
The Patel family went to the same restaurant and bought five of the same Pizzas, six of the same Chillies and seven of the same Pastas. They paid $£ 107$ in total.
How much more does a Pizza cost than a Pasta?
Solution
Let the prices in pounds of one Pizza, one Chilli and one Pasta be $x, y, z$ respectively. Then, $2 x+3 y+4 z=53 \ldots[1]$. Also, $5 x+6 y+7 z=107 \ldots[2]$.
$$
\begin{array}{l}
{[1] \times 2: 4 x+6 y+8 z=106 \ldots} \\
{[2]-[3]: x-z=1 .}
\end{array}
$$

So a Pizza costs $£ 1$ more than a Pasta.