A market stall sells rice so that the cost is directly proportional to the mass bought. A customer pays \(\pounds 6.25\) for 2.5 kg of rice. The stallholder...
Question 1 Report
A market stall sells rice so that the cost is directly proportional to the mass bought. A customer pays \(\pounds 6.25\) for 2.5 kg of rice. The stallholder wants to check the price before weighing a larger bag for a catering order.
- Work out the cost of 4 kg of rice. (3)
Answer Details
Direct proportion means cost divides by mass to give a constant price per kilogram; once that constant is found from the known pair of values, it can be used to price any other mass.
\[ k = 6.25\div2.5 = \pounds2.50 \text{ per kg} \] [1 mark]
Cost of \(4\) kg: \[ 2.50\times4 = \pounds10.00 \] [2 marks]
Because cost is directly proportional to mass, doubling or scaling the mass by any factor scales the cost by exactly the same factor, which is the property that makes the price-per-kilogram method valid here.
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