At a bookstore, 8 points are earned for every $3 spent. For every $60 spent, there is an additional 150 bonus points. Ming wants to earn at least 1000 points to exchange for a book voucher.
- How many points does Ming earn when he spends $60?
- What is the least amount of money Ming needs to spend to earn at least 1000 points?
Need a hint?
Work out the points from full $60 blocks first, including the bonus. Then find how many $3 lots are needed for the remaining points, rounding up.
Worked answer
- (a) $60 ÷ $3 = 20 lots of $3, so 20 × 8 = 160 points from spending.
- (a) Add the bonus: 160 + 150 = 310 points.
- (b) Each $60 gives 310 points, so $180 (3 lots of $60) gives 3 × 310 = 930 points.
- (b) Still need 1000 − 930 = 70 points, and each $3 gives 8 points.
- (b) 8 lots of $3 give only 64 points, so 9 lots are needed: 9 × $3 = $27, giving 72 points.
- (b) Total spent: $180 + $27 = $207.
The mistake this question tests
Calculation slip
Pupils often forget the 150 bonus points, or stop at 8 lots of $3 for the leftover 70 points because 70 ÷ 8 is not a whole number, which leaves them short of 1000.
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