The Fundraiser Total That Does Not Add Up
A class sells 240 raffle tickets at $2 each and 60 cupcakes at $3 each. They also receive a $50 donation. Their target is $700. The treasurer writes in the report: 'We raised $480 from tickets, $180 from cupcakes and $50 donation, so $710 in total, beating our $700 target by $10.' A parent checks the numbers before the report is printed. Tickets are sold in books of 10, and one full book was returned unsold and must be subtracted from the 240 counted.
1. Check the treasurer's arithmetic and the effect of the returned book. What is the true total, and does it beat the target?
Read the worked answer
Step 1: Correct the ticket count. One book of 10 was returned, so tickets sold = 240 − 10 = 230.
Step 2: Ticket money. 230 × $2 = $460, not $480.
Step 3: Cupcakes. 60 × $3 = $180. Correct.
Step 4: Add the donation. $460 + $180 + $50 = $690.
Step 5: Compare to target. $690 is $10 short of $700, not $10 over.
The treasurer made two errors: they used the pre-return ticket count, and they then reported the total as beating the target. The true figure is $690, so the report must say the class fell $10 short - or note that a further $10 would close the gap.
2. The class wants to sell more cupcakes to reach $700. How many extra cupcakes at $3 each are needed, and what is the smallest number that clears the target?
Read the worked answer
Gap: $700 − $690 = $10.
Cupcakes needed: $10 ÷ $3 = 3.33, so 3 cupcakes give only $9 and leave the class at $699 - still $1 short.
Smallest number that clears the target: 4 cupcakes. 4 × $3 = $12, bringing the total to $690 + $12 = $702.
So the answer is 4, not 3, because you cannot sell a third of a cupcake. The report should say 'four more cupcakes' and show the new total of $702, which beats $700 by $2.