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Algebra, STD2 EQ-Bank 10

The cost (\(C\)) of copper wire varies directly with the length (\(L\)) in metres of the wire.

This relationship is modelled by the formula \(C = kL\), where \(k\) is a constant.

A 250 metre roll of copper wire costs $87.50.

  1. Show that the value of \(k\) is 0.35.   (1 mark)
  2. A builder has a budget of $140 for copper wire. Calculate the maximum length of wire that can be purchased.   (2 marks)
Show Answers Only

a.    \(C=kL\)

\(\text{When } C = 87.50 \text{ and } L = 250:\)

\(87.50\) \(=k \times 250\)
\(k\) \(=\dfrac{87.50}{250}\)
\(k\) \(=0.35\ \text{(as required)}\)

b.     \(400\ \text{m}\)

Show Worked Solution

a.    \(C=kL\)

\(\text{When } C = 87.50 \text{ and } L = 250:\)

\(87.50\) \(=k \times 250\)
\(k\) \(=\dfrac{87.50}{250}\)
\(k\) \(=0.35\ \text{(as required)}\)

 
b.    \(C = 0.35L\)

\(\text{When } C = 140:\)

\(140\) \(=0.35\times L\)
\(L\) \( =\dfrac{140}{0.35}\)
  \(=400\ \text{m}\)

    
\(\therefore\ \text{The builder can purchase } 400 \text{ metres of wire.}\)