Project: a dream budget

Your event, your numbers

The second-last lesson — and no new topic. Instead a project: you will plan your own event and calculate a complete budget for it. A trip with friends, a birthday party, a LAN party, a weekend on bikes. What you want.

Why a budget? Because it is maths you will do your whole life — and because it hides half of this level: percents, money calculating, ratios, a chart, estimates. Only this time the numbers are not from a question. They are yours.

Rules of the project: the event has a budget ceiling (how much you may spend in total — say 2 000 Kč), at least five items (transport, food, tickets…), a 10 % reserve for unexpected costs and at the end a pie chart where you can see what bites how much.

The output is one page: a table of items with prices, calculations, a chart and a conclusion — did you fit into the ceiling?

This is a dry run for adulthood in small. And quite fun, you will see.

Ema, Adam and Jonáš plan a one-day bike trip with a budget of 500 Kč per person. Ema is treasurer: “Train there 89, back 89, lunch 150, ice cream 40, lookout tower ticket 60. Sum 428.” Jonáš waves a hand: “Easy, 72 Kč to spare!” Ema shakes her head: “A reserve of 10 % of 500 is 50 Kč — for a puncture or a forgotten bottle. So to spare is 22.” Adam laughs: “A treasurer with a reserve is why we come back from trips without debts.”

Building a budget step by step

Step 1: Set the ceiling. How much the event may cost in total. Say 2 000 Kč for four people.

Step 2: List the items. At least five. Transport, food and drink, tickets, kit, treats… By each a price — looked up, or a marked estimate.

Step 3: Subtract the reserve in advance. Reserve = 10 % of the ceiling: 2 000 · 0.1 = 200 Kč. For spending, 1 800 Kč is left. The reserve is put aside AT THE START — what is left at the end is not a reserve, that is luck.

Step 4: Add the items and compare. Sum ≤ 1 800? Done. Sum more? Cut or look for a cheaper version — that is exactly budgeting.

Step 5: Calculate the shares. Each item: share = item / total sum · 100. Transport 600 Kč of 1 800: 600/1800 = 33.3 %.

Step 6: Draw a pie chart. Percents times 3.6 = degrees of a sector (lesson 23). Check: sum 100 %.

Step 7: Write a conclusion. Two sentences: did the budget fit the ceiling? Which item eats the most and could it be thinned?

Per person then: total / number of people. And if you saved in advance: how many weeks at 100 Kč a week? That is a linear function from lesson 9 — everything meets.

Example 1: a trip budget with a ceiling

Question: A trip for 4 people, ceiling 2 000 Kč. Items: train 4 · 120 = 480 Kč, lunches 4 · 140 = 560 Kč, tickets 4 · 80 = 320 Kč, snacks 200 Kč, a map and bits 100 Kč. Does it fit even with a 10 % reserve?

Method: Reserve: 2 000 · 0.1 = 200 Kč. To spend: 1 800 Kč.

Sum of items: 480 + 560 + 320 + 200 + 100 = 1 660 Kč.

Compare: 1 660 ≤ 1 800. It fitted, 140 Kč of slack is left.

Answer: Yes. Total with the reserve 1 860 Kč of 2 000 Kč. Per person: 1 860/4 = 465 Kč.

Example 2: shares and a chart

Question: From the budget above calculate the percent shares of the items (of 1 660 Kč) and the degrees for a pie chart.

Method: Train: 480/1660 ≈ 28.9 % → 28.9 · 3.6 ≈ 104°.

Lunches: 560/1660 ≈ 33.7 % → 121°. Tickets: 320/1660 ≈ 19.3 % → 69°. Snacks: 200/1660 ≈ 12.0 % → 43°. Bits: 100/1660 ≈ 6.0 % → 22°.

Check: 28.9 + 33.7 + 19.3 + 12 + 6 = 99.9 % (rounding) and degrees ≈ 359° — fine.

Conclusion from the chart: lunches and the train eat over 60 % of the budget. Who wants to save deals with food from home, not a cheaper ice cream.

Example 3: when the budget does not fit

Question: A party with a ceiling of 1 500 Kč: pizza 800, a cake 450, decorations 250, drinks 200, games 150. Reserve 10 %. What to do?

Method: To spend: 1 500 − 150 = 1 350 Kč. Sum: 800 + 450 + 250 + 200 + 150 = 1 850 Kč. Overflow: 500 Kč.

I cut by priorities: a homemade cake instead of a bought one (450 → 150, saved 300), homemade decorations (250 → 100, saved 150), one less pizza (800 → 720, saved 80).

New sum: 720 + 150 + 100 + 200 + 150 = 1 320 ≤ 1 350. It fitted.

Answer: Budgeting is not “having enough money”, but deciding what is important. You cut from items where a cheaper version is almost as good.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 시작 with ten. When it goes well, add more.

Practise percents of a number — a reserve, shares of items and discounts are exactly that. Write a whole number.

Practise the questions

Project on paper

Now you and your event. One page, all the numbers yours.

1. Pick an event and set a ceiling (300–3 000 Kč, after a talk with parents if you like). Put aside a 10 % reserve and write how much is left to spend.

2. Build a table of at least five items with looked-up or marked estimated prices. Add and compare with the ceiling. If it overflows, cut by priorities and write what and why.

3. Calculate the percent shares of the items and draw a pie chart (percents times 3.6 = degrees, check 100 %).

4. Write a three-sentence conclusion: did you fit? What eats the most? And a bonus: how many weeks of saving at 150 Kč a week would pay for the event?

Now you 💪

1. A 10 % reserve is put aside in advance, not calculated at the end.
2. Each price is looked up, or honestly marked as an estimate.
3. The chart matches: the shares add up to 100 % and match the table.

What to take from this lesson

• A budget = a ceiling, items, a 10 % reserve in advance, a check of the sum.
• Percents in action: a reserve, shares of items, discounts.
• When you do not fit, you cut by priorities — that is the heart of budgeting.
• A pie chart shows the budget-eaters at a glance.
• Saving for a goal is a linear function: weeks times an amount.

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