Canister inventory and graphical solution

Canister inventory and graphical solution

Secondary 2
8 marks
TGM Original Questions

A laboratory storeroom contains \(44\) canisters with a total capacity of \(172\) litres. Small canisters hold \(3\) litres and large canisters hold \(5\) litres. Let \(s\) be the number of small canisters and \(l\) be the number of large canisters.

  1. Form two equations in \(s\) and \(l\).[2]
  2. Copy and complete the following tables of values of \(s\) and \(l\) for the equations \(s+l=44\) and \(3s+5l=172\).
    For the equation \(s+l=44\):
    \(s\)\(0\)\(22\)\(44\)
    \(l\)
    For the equation \(3s+5l=172\):[2]
    \(s\)\(4\)\(24\)\(44\)
    \(l\)
  3. On the grid provided below, using the numbered axis scales, draw and label the graphs of \(s+l=44\) and \(3s+5l=172\) for \(0\leq s\leq50\) and \(0\leq l\leq50\).[3]
  4. Hence, use the graphs to find the numbers of small and large canisters.[1]

Solution:

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Answer:(a) \(s+l=44,\ 3s+5l=172\). (b) First table: \(l=44,22,0\); second table: \(l=32,20,8\). (c) See the completed graphs. (d) 24 small and 20 large canisters.

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