A bakery mixes flour and butter in the ratio \(5 : 2\) by mass. One batch of pastry uses \(m\) grams of flour. Write the mass of butter in terms of \(m\). (...
Question 1 Report
A bakery mixes flour and butter in the ratio \(5 : 2\) by mass. One batch of pastry uses \(m\) grams of flour.
- Write the mass of butter in terms of \(m\). (1)
- The whole batch has mass 2100 grams. Find \(m\). (2)
- Write down the mass of butter in that batch. (1)
Answer Details
The ratio \(5 : 2\) means that for every \(5\) parts of flour there are \(2\) parts of butter, so the butter is \(\frac{2}{5}\) of the flour by mass.
(a)
\[\text{butter} = \frac{2m}{5} \text{ grams}\][1]
(b) The batch is flour plus butter, and the two must be written over a common denominator before adding. Since \(m = \frac{5m}{5}\):
\[m + \frac{2m}{5} = \frac{5m + 2m}{5} = \frac{7m}{5} = 2100\][1]
Multiplying both sides by \(5\) and dividing by \(7\):
\[7m = 10500 \implies m = 1500 \text{ grams}\][1]
(c) The butter is what remains of the batch once the flour is accounted for:
\[2100 - 1500 = 600 \text{ grams}\][1]
This agrees with the expression from part (a), since \(\frac{2 \times 1500}{5} = 600\) grams.
The whole batch is \(5 + 2 = 7\) parts, so each part is \(2100 \div 7 = 300\) grams, giving \(5 \times 300 = 1500\) g of flour and \(2 \times 300 = 600\) g of butter. That parts method is a quick independent check. The error to avoid is treating \(m\) as the total mass rather than the mass of flour, which the question defines explicitly.
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