A farmer harvests a large field of wheat during an unusually dry autumn and sells \(\frac{5}{8}\) of the whole crop at a busy local market before the weathe...
Question 1 Report
A farmer harvests a large field of wheat during an unusually dry autumn and sells \(\frac{5}{8}\) of the whole crop at a busy local market before the weather finally turns, leaving 90 tonnes of wheat stored in the barn for winter feed.
- Work out the total mass, in tonnes, of wheat harvested from the field. (3)
Answer Details
This question tests working backwards from a known remainder to find an original total, using the fraction that is left after a portion is sold.
Since \(\frac{5}{8}\) of the crop was sold, the fraction left in the barn is \(1 - \frac{5}{8} = \frac{3}{8}\), and this fraction corresponds to the 90 tonnes stored. [1]
If \(\frac{3}{8}\) of the harvest is 90 tonnes, then one eighth of the harvest is
\[90 \div 3 = 30 \text{ tonnes}.\][1]
The whole harvest (eight eighths) is therefore
\[30 \times 8 = 240 \text{ tonnes}.\][1]
Whenever a quantity is described as a fraction of an unknown total, first identify what fraction the known amount represents, then scale from one part up to the whole; scaling from the wrong fraction (using \(\frac{5}{8}\) instead of \(\frac{3}{8}\)) is the main pitfall here.
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