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Algebra, STD2 EQ-Bank 24

A bookshop sold a number of biographies at a weekend sale.

Hardcover biographies \((h)\) sold for $25 each and paperback biographies \((p)\) sold for $12 each.

A total of 11 biographies were sold, with total sales revenue of $210.

  1. Write two equations, in terms of \(h\) and \(p\), to represent this information.   (1 mark)

  2. Determine the number of hardcover biographies and the number of paperback biographies sold.   (2 marks)

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\(h=6, \ p=5\)

Show Worked Solution

a.    \(25h+12p=210\ …\ (1)\)

\(h+p=11\ …\ (2)\)
 

b.    \(\text{Rearranging (2) above:}\)

\(h=11-p\)

\(\text{Substitute}\ \ h=9-p\ \ \text{into (1):}\)

\(25(11-p)+12p\) \(=210\)
\(275-25p+12p\) \(=210\)
\(13p\) \(=275-210=65\)
\(p\) \(=5\)

 
\(\text{Substitute}\ \ p=5\ \ \text{into (2):}\)

\(h=11-5=6\)

\(\therefore\ \text{6 hardcover and 5 paperback biographies were sold.}\)