The length of bunting for the sports day finish line is directly proportional to the number of flags used, where \(y\) metres is the length and \(x\) is the...
Question 1 Report
The length of bunting for the sports day finish line is directly proportional to the number of flags used, where \(y\) metres is the length and \(x\) is the number of flags. When \(x = 15\), \(y = 9\).
- Work out \(k\) in \(y = kx\). (1)
- Work out the length of bunting needed for 40 flags. (2)
- Find the number of flags that would need 3.6 m of bunting. (1)
Answer Details
This question tests direct proportion expressed with a formula, \(y=kx\), where \(k\) must first be found from one known pair of values.
(a) Substituting \(x=15\), \(y=9\) into \(y=kx\):
\[9=15k \implies k=\frac{9}{15}=0.6 \text{ <b>[1]</b>}\](b) Using \(y=0.6x\) with \(x=40\):
\[y=0.6\times 40=24 \text{ m <b>[2]</b>}\](c) Setting \(y=3.6\) and solving for \(x\):
\[x=\frac{3.6}{0.6}=6 \text{ flags <b>[1]</b>}\]Once \(k=0.6\) is found in part (a), it is the fixed length of bunting per flag; multiplying by the number of flags gives the total length, and dividing a given length by \(k\) gives the number of flags, which is exactly what parts (b) and (c) do in opposite directions.
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