The pie chart shows how \(1080\) people travel to work. (a) Work out the number of these people who travel by car. [2] (b) Work out the percentage of these ...

In a pie chart the whole circle, \(360^\circ\), represents everybody: here the \(1080\) people. Each sector angle is therefore a fraction of \(360\), and that same fraction applies to the \(1080\) people. The car sector measures \(140^\circ\), and the walk and train sectors each measure \(60^\circ\).

(a) The car sector is \(\frac{140}{360}\) of the whole, so it represents that fraction of the people:

\[ \frac{140}{360}\times 1080 \] [M1]

\[ =420 \]

\(420\) people travel by car. [A1]

A quick check: \(1080\div 360=3\), so every degree stands for \(3\) people, and \(140\times 3=420\).

(b) The percentage comes straight from the angle, since the fraction of the circle is the fraction of the people:

\[ \frac{60}{360}\times 100 \] [M1]

\[ =16.666\ldots \]

Correct to \(1\) decimal place, \(16.7\%\) of the people walk. [A1]

(c) First find how many travel by train now, then apply the increase. An increase of \(15\%\) has multiplier \(1.15\).

\[ \frac{60}{360}\times 1080=180\qquad\text{then}\qquad 180\times 1.15 \] [M1]

\[ =207 \]

\(207\) people are expected to travel by train next year. [A1]

The increase applies to the \(180\) train travellers, not to the \(1080\) total. Always identify the group being changed before applying the multiplier.