Fair Splits in the Real World
Splitting a food order, giving out extra-credit points, sharing a town's park money: three problems where you decide how to be fair and explain your thinking.
Work through each problem. Use the hint if you're stuck, and check your answers when you're done with each part.
Four friends order food together. The total comes to $60.
• Arlo ordered $20 worth of food
• Bea ordered $15
• Carmen ordered $15
• Dev ordered $10
If they split the bill equally, how much does each person pay?
Show answer
$60 ÷ 4 = $15 each.
If each person pays for what they actually ordered, how much does each pay?
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Arlo: $20, Bea: $15, Carmen: $15, Dev: $10.
Which way feels fairer to you here? Why?
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Both work. Equal split is simpler and treats everyone the same, like members of the same team. Proportional feels fairer when people ordered very different amounts. There's no wrong answer — just pick one and explain why.
Does your answer change if they're close friends versus people who don't know each other that well?
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Often yes. Close friends might just split it equally and not think twice about it. People who don't know each other as well might prefer everyone paying for what they ordered, so nobody feels like they paid for someone else's food. Who you're with can change what feels fair.
HintShowHide
For (a): divide the total equally among 4 people. For (b): each person's share is just what they ordered — no division needed. For (c) and (d): think about who these people are to each other, and what "fair" means in that situation.
A teacher has 24 extra-credit points to give out to three students who all helped set up the science fair.
• Fatima worked for 6 hours
• Gus worked for 4 hours
• Hana worked for 2 hours
How would you divide the points equally?
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24 ÷ 3 = 8 points each.
How would you divide them based on hours worked?
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Total hours: 6 + 4 + 2 = 12.
Fatima: (6 ÷ 12) × 24 = 12 points.
Gus: (4 ÷ 12) × 24 = 8 points.
Hana: (2 ÷ 12) × 24 = 4 points.
Is there any other information you'd want to know before deciding which way to split the points?
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Good answers include: Was the quality of each person's work different? Did anyone do harder jobs? Did any of the students have other things going on that made it hard to stay longer? Was helping their own choice, or were they asked to? Any of these could change which split feels right.
HintShowHide
For (b): start by adding up the total hours (6 + 4 + 2). Each person's fraction is their hours ÷ total hours. Multiply that fraction by 24.
A town has $900,000 to spend on improvements to its parks. Three neighborhoods will share the money:
• Riverside: 1,000 people
• Midtown: 5,000 people
• Hillcrest: 4,000 people
If the money is split equally between neighborhoods, how much does each get?
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$900,000 ÷ 3 = $300,000 per neighborhood.
If it's split based on how many people live in each neighborhood, how much does each get?
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Total: 1,000 + 5,000 + 4,000 = 10,000 people.
Riverside: (1,000 ÷ 10,000) × $900,000 = $90,000.
Midtown: (5,000 ÷ 10,000) × $900,000 = $450,000.
Hillcrest: (4,000 ÷ 10,000) × $900,000 = $360,000.
What are two reasons for splitting equally? Two reasons for splitting by how many people live there?
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Equal: Every neighborhood matters, no matter how big or small. If we always give money based on size, smaller neighborhoods will keep getting less.
By population: More people are helped per dollar. Every person gets the same amount no matter which neighborhood they live in.
What else would you want to know about these neighborhoods before deciding?
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Good answers include: Does one neighborhood already have nice parks while another's are falling apart? How big are the parks in each neighborhood? Can families in some neighborhoods pay to fix parks on their own? Has one neighborhood already gotten money recently?
HintShowHide
For (b): total = 1,000 + 5,000 + 4,000. Each neighborhood's share = (its number of people ÷ total) × $900,000. For (c): try to think of the strongest reason for each side, not just the one you agree with.