Two steel beams stored on a construction site have lengths in the ratio \(3 : 5\). When the site foreman measures them, the longer beam turns out to be 2 m ...
Question 1 Report
Two steel beams stored on a construction site have lengths in the ratio \(3 : 5\). When the site foreman measures them, the longer beam turns out to be 2 m longer than the shorter beam.
Solve to find the length of each beam. (3)
Answer Details
This question tests setting up and solving a linear equation from a ratio together with a difference between the two quantities.
Since the beam lengths are in the ratio \( 3 : 5 \), they can be written as \( 3x \) and \( 5x \) metres for some number \( x \). [1 mark]
The longer beam is 2 m longer than the shorter one, so
\[ 5x - 3x = 2 \]
\[ 2x = 2 \]
\[ x = 1 \] [1 mark]
Substituting \( x = 1 \) back into the two expressions gives the shorter beam as \( 3 \times 1 = 3 \) m and the longer beam as \( 5 \times 1 = 5 \) m. [1 mark]
As a check, \( 5 - 3 = 2 \) m, which matches the given difference, and the beams are indeed in the ratio \( 3 : 5 \).
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