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Systems of Equations · Part 3 of 3
3 exam-style questions with model answers, plus 4 quick multi-choice questions — every question on this part of the standard, grouped by the 1 page of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A farmer buys 15 bags of feed, some at $28 each and the rest at $45 each, spending $536 in total. Form a system of equations and find how many of each kind were bought.
A courtyard is to be paved with a rectangular area of paving surrounded by a border of uniform width. The paved rectangle measures 12 m by 8 m, and the total area including the border is 165 m2. Find the width of the border, and explain why only one of your solutions is used.
A fruit grower sells apples at $4/kg and pears at $6/kg. Last week the total revenue was $1,200 from 250 kg of fruit. This week the grower wants revenue of at least $1,400 from at most 260 kg, and can pick at most 180 kg of apples. Determine whether this week's targets are achievable, and analyse the trade-off the grower faces.