A farm cooperative stores grain in a large silo. During the autumn harvest, \(\frac{2}{5}\) of the silo's capacity is filled. Over the winter, a further \(\...
Question 1 Report
A farm cooperative stores grain in a large silo. During the autumn harvest, \(\frac{2}{5}\) of the silo's capacity is filled. Over the winter, a further \(\frac{1}{4}\) of the silo's capacity is filled with a second harvest.
- Work out the fraction of the silo's capacity filled after both harvests. (2)
- The silo is then found to have 49 tonnes of empty space remaining. Work out the total capacity of the silo, in tonnes. (3)
- Work out the mass of grain added during the second harvest, in tonnes. (1)
- A minimum of 150 tonnes of empty space is required for safe ventilation. State, with a reason, whether the silo currently meets this requirement. (1)
Answer Details
(a) This part tests adding fractions with different denominators. Writing both fractions over the common denominator 20 gives \(\frac{2}{5} = \frac{8}{20}\) and \(\frac{1}{4} = \frac{5}{20}\), so the silo is \(\frac{8}{20} + \frac{5}{20} = \frac{13}{20}\) full after both harvests [2 marks].
(b) The empty fraction is \(1 - \frac{13}{20} = \frac{7}{20}\), and this equals the 49 tonnes of empty space [2 marks]. Dividing 49 by \(\frac{7}{20}\) (multiplying by its reciprocal, \(\frac{20}{7}\)) gives the total capacity: \(49 \div \frac{7}{20} = 49 \times \frac{20}{7} = 140\) tonnes [1 mark].
(c) The mass added during the second harvest is \(\frac{1}{4} \times 140 = 35\) tonnes [1 mark].
(d) Since the silo needs at least 150 tonnes of empty space for safe ventilation and only 49 tonnes are empty, and \(49 < 150\), the silo does not currently meet this requirement [1 mark].
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