Petrol Station
Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?
Age
14 to 16
Challenge level
Problem
Andrea's petrol tank holds up to $44$ litres of fuel. She goes to the garage when her tank is a quarter full and fills up the tank until it is two-thirds full. How many litres of petrol does she put in the tank?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $18\frac13$
Finding the amounts of petrol
tank: $44$ litres $\frac14$ of $44 = 11$
$\frac13$ of $44 = 44\div3 = 14\frac23$
$\frac23$ of $44=44-14\frac23=29\frac13$
$29\frac13-11=18\frac13$
Finding the quantity as a fraction
The volume of petrol that Andrea put in is the difference between $\frac{2}{3}$ and $\frac{1}{4}$ of a tank.
$\frac23-\frac14=\frac{5}{12}$
$\frac{5}{12}$ of $44$ litres $=\frac{5}{12} \times 44 = \frac{5\times 44}{12}=\frac{5\times11}{3} = \frac{55}{3}=18\frac{1}{3}$