A festival's organisers set a budget of £4800. They spend \(\dfrac{1}{3}\) of the budget on hiring artists and \(\dfrac{1}{4}\) of the budget on staging. Wo...
Question 1 Report
A festival's organisers set a budget of £4800. They spend \(\dfrac{1}{3}\) of the budget on hiring artists and \(\dfrac{1}{4}\) of the budget on staging.
- Work out the fraction of the budget that remains after these two payments. (2)
- Work out the amount of money that remains. (1)
Answer Details
(a) The fraction remaining is the whole budget, \(1\), minus the two fractions already spent. Writing all three with the common denominator \(12\): \(1-\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{12}{12}-\dfrac{4}{12}-\dfrac{3}{12}=\dfrac{5}{12}\). [2 marks]
(b) Applying this fraction to the total budget: \(4800\times\dfrac{5}{12}\). Dividing \(4800\) by \(12\) gives \(400\), and multiplying by \(5\) gives \(\pounds2000\) remaining. [1 mark]
Converting every fraction to the same common denominator before subtracting is essential whenever fractions with different denominators, here thirds and quarters, are being combined.
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