Broken stock and target profit

Broken stock and target profit

Secondary 2
10 marks
TGM Original Questions

Optional extension

A trader spends \(\$540\) on identical vases at \($x\) each. Six break. Every remaining vase is sold for \($(x+3)\), producing a total profit of \(\$108\).

  1. Write the number of vases bought.[2]
  2. Write the total sales receipt.[2]
    1. Form an equation in \(x\) and reduce it to a quadratic.[2]
    2. Solve it and reject the inadmissible root.[2]
  4. Find the number of vases sold.[2]

Solution:

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Answer:(a) \(\dfrac{540}{x}\) (b) \((\dfrac{540}{x}-6)(x+3)\) (c)(i) \((\dfrac{540}{x}-6)(x+3)=648\), so \(x^2+21x-270=0\) (ii) \(x=9\) (d) \(54\).

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