A phone company has \(180\) customers split between three tariffs, shown in the pie chart below. The Pay-as-you-go sector has an angle of \(90^\circ\) and t...
Question 1 Report
A phone company has \(180\) customers split between three tariffs, shown in the pie chart below. The Pay-as-you-go sector has an angle of \(90^\circ\) and the Basic sector has an angle of \(120^\circ\); the Premium sector's angle is not marked. (a) Work out the angle of the Premium sector. (1) (b) Work out the number of customers on the Premium tariff. (2)
Answer Details
A pie chart divides a full turn of \( 360^\circ \) between all the categories, so an unmarked sector's angle is found by subtracting the known angles from \( 360^\circ \), and converting an angle to a quantity uses the same fraction of the total that the angle is of the full circle.
(a) Since the three sectors must add up to a full turn, the Premium sector's angle is \( 360-90-120=150^\circ \) [1 mark].
(b) The Premium sector represents the fraction \( \dfrac{150}{360} \) of all 180 customers: \( \dfrac{150}{360}\times 180=75 \) customers [2 marks].
As a check, the same method applied to the other two sectors gives \( \dfrac{90}{360}\times180=45 \) Pay-as-you-go and \( \dfrac{120}{360}\times180=60 \) Basic customers; adding all three, \( 45+60+75=180 \), confirms every customer is accounted for.
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