A taxi firm's fare income for one day is \(\pounds T\). Of this, \(\dfrac{2}{5}\) goes on fuel and \(\dfrac{1}{6}\) goes on maintenance, as shown in the dia...
Question 1 Report
A taxi firm's fare income for one day is \(\pounds T\). Of this, \(\dfrac{2}{5}\) goes on fuel and \(\dfrac{1}{6}\) goes on maintenance, as shown in the diagram. The driver keeps the rest, and this comes to \(\pounds58.50\).
- Work out the fraction of \(T\) that the driver keeps. (1)
- Form and solve an equation to find \(T\). (3)
Answer Details
(a) The fraction the driver keeps is what remains once the fuel and maintenance fractions are subtracted from the whole. Writing both with the common denominator \(30\): \(1-\dfrac{2}{5}-\dfrac{1}{6}=\dfrac{30}{30}-\dfrac{12}{30}-\dfrac{5}{30}=\dfrac{13}{30}\). [1 mark]
(b) Since this fraction of \(T\) comes to \(\pounds58.50\): \(\dfrac{13}{30}T=58.50\). [1 mark] Multiplying both sides by the reciprocal, \(\dfrac{30}{13}\), gives \(T=58.50\times\dfrac{30}{13}\). [1 mark] This gives \(T=\pounds135\). [1 mark]
Multiplying by the reciprocal of \(\dfrac{13}{30}\) is the standard way to "undo" a fraction of an unknown total, recovering the full fare income, \(\pounds135\), from knowing only what the remaining \(\dfrac{13}{30}\) share amounts to.
Download The App On Google Playstore
Everything you need to excel in your exams
