The Rink Fundraiser: Deciding Which Total to Trust
The Grade 6 class is selling chocolate bars to pay for a skating trip. A full case holds 30 bars. On Monday they sell 2 full cases plus 7 extra bars. On Tuesday they sell 1 full case, then return 4 damaged bars to the supplier. On Wednesday a parent donates 3 half-cases, and the class sells 46 bars. The teacher writes the running total as 60 + 7 + 30 − 4 + 45 − 46. Two students disagree about the answer: Maya says 92 bars remain, and Dev says 92 is wrong because 'you cannot subtract bars you sold from bars you have if the donated half-cases were not opened.' The supplier charges $1.25 per bar and the trip costs $540.
1. Evaluate the teacher's expression step by step. Is Maya's total of 92 bars correct? Show how each number in the expression connects to the story.
Read the worked answer
Work left to right, keeping track of what each term means:
- 60 = 2 cases sold Monday (2 × 30)
- +7 = the 7 extra bars sold Monday
- +30 = 1 case sold Tuesday
- −4 = damaged bars returned, so they leave the stock count
- +45 = 3 half-cases donated (3 × 15)
- −46 = bars sold Wednesday
Compute: 60 + 7 = 67; 67 + 30 = 97; 97 − 4 = 93; 93 + 45 = 138; 138 − 46 = 92.
Maya is correct that the arithmetic gives 92. Dev's objection confuses two ideas. Whether a half-case is opened does not change how many bars it contains; 3 half-cases is 45 bars either way. The expression is a net-change model: start from zero, add what comes in, subtract what goes out. The order of adding and subtracting does not change the result, so the total of 92 bars on hand is valid.
2. The class needs $540. Using the 92 bars on hand plus the money already collected from bars sold, decide whether they will reach the goal. State any assumption you must make.
Read the worked answer
Count bars sold: Monday 67, Tuesday 30, Wednesday 46, total 143 bars sold.
Money collected: 143 × $1.25 = $178.75.
If the 92 remaining bars all sell: 92 × $1.25 = $115.00.
Combined: $178.75 + $115.00 = $293.75, which is far short of $540.
Assumption: every remaining bar sells at full price and the 4 damaged bars earn nothing. Even under that best case the class is about $246 short, so they need another fundraiser or more cases. A good answer names the assumption rather than silently ignoring the damaged bars or the unsold stock.