Friday fries: break-even and a loyalty card
Aria is a Year 12 student who runs a loaded-fries stall every Friday lunchtime at her school. The school charges a fixed site fee of $85 per Friday, payable whether she trades or not. Ingredients cost $2.10 per serve, and she sells each serve for $6.50. She starts each Friday with a $140 float for change, which she takes home again at the end of the day. On a typical Friday she sells 70 serves, but wet weather can cut this to 30. Aria is considering a loyalty card: buy five serves and get the sixth free. She estimates that about one in every six serves would then be given away, while total sales would rise to about 85 serves on a fine Friday. She wants to know how many serves she must sell just to cover the site fee, how many she needs for a $300 profit, and whether the loyalty card is worth it.
1. Calculate Aria's break-even number of serves on a normal Friday with no loyalty card. Then calculate how many serves she needs to make a $300 profit. Show each step and explain any rounding.
Read the worked answer
Contribution per serve = selling price − ingredient cost = $6.50 − $2.10 = $4.40. The $85 site fee is fixed, and the $140 float is not a cost because Aria takes it home again.
Break-even: $85 ÷ $4.40 = 19.32 serves. She cannot sell 0.32 of a serve, so she must sell 20 serves to cover the fee. At 19 serves her margin is 19 × $4.40 = $83.60, which is $1.40 short.
$300 profit target: the margin must cover the fee plus profit: ($85 + $300) ÷ $4.40 = $385 ÷ $4.40 = 87.5 serves, so 88 serves. Check: 88 × $4.40 = $387.20; $387.20 − $85 = $302.20, which reaches the target. At 70 serves her profit is 70 × $4.40 − $85 = $308 − $85 = $223.
2. Evaluate the loyalty card using Aria's estimate that on a fine Friday she sells 85 serves, of which one in six is free. Calculate the effective average contribution per serve, the new break-even, and the profit at 85 serves. Should Aria adopt the card? Justify with numbers.
Read the worked answer
With the card, in every 6 serves she gives away 6 and is paid for 5, so revenue per 6 serves = 5 × $6.50 = $32.50, while ingredients cost 6 × $2.10 = $12.60. Contribution per 6 serves = $32.50 − $12.60 = $19.90, or $19.90 ÷ 6 = $3.3167 per serve on average.
New break-even = $85 ÷ $3.3167 = 25.63, so 26 serves (up from 20).
Profit at 85 serves: 85 × $3.3167 − $85 = $281.92 − $85 = $196.92. Without the card, 70 serves gave $223. So on these estimates the card reduces profit, even though sales rise by 15 serves.
Sales needed to match $223 profit with the card: (223 + 85) ÷ 3.3167 = 308 ÷ 3.3167 = 92.9, so about 93 serves. The card is only worth it if it lifts sales from 70 to at least 93, or if it brings extra customers who also buy drinks (not included here). Otherwise keep the simple pricing.
3. Aria's friend says, 'You only need to sell 20 serves to make money, so selling 30 in wet weather is fine.' Evaluate this claim for both the no-card and loyalty-card options.
Read the worked answer
At 30 serves with no card: 30 × $4.40 = $132; $132 − $85 = $47 profit. That is positive, but thin: two fewer serves and she is at break-even, and a wet day with 20 serves gives 20 × $4.40 − $85 = $3.
With the card, break-even is 26 serves, so 30 serves would give 30 × $3.3167 − $85 = $99.50 − $85 = $14.50 only, assuming the same 30 serves include 5 free ones. The friend's claim is only true in the no-card case, and 'making money' at $47 is not the same as covering her time and risk. The fixed fee is charged whether she trades or not, so a wet Friday can still make a loss if sales fall below 20.