At a garden centre, 5 points are earned for every $4 spent. For every $40 spent, an additional 60 bonus points are given. Mr Rahim wants to earn 475 points to exchange for a plant set.
- How many points does Mr Rahim earn altogether when he spends exactly $40?
- What is the least amount of money Mr Rahim needs to spend to earn at least 475 points?
Need a hint?
First find the points for every $40 spent, bonus included. See how many whole $40 lots fit into 475 points, then deal with the points left over.
Worked answer
- (a) $40 has 40 ÷ 4 = 10 lots of $4, so 10 × 5 = 50 points.
- Add the bonus: 50 + 60 = 110 points for every $40 spent.
- (b) 4 lots of $40 give 4 × 110 = 440 points, and this costs 4 × $40 = $160.
- Points still needed: 475 − 440 = 35 points.
- 35 ÷ 5 = 7 lots of $4, so he spends 7 × $4 = $28 more.
- $28 is less than $40, so no extra bonus is earned and nothing cheaper works.
- Least amount: $160 + $28 = $188.
The mistake this question tests
Calculation slip
Many pupils forget the bonus points and work out 475 ÷ 5 × $4 = $380. Others treat the 35 leftover points as $35 instead of finding how many $4 lots give 35 points.
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