Mathematics • Year 8 • Unit 1 • Lesson 20
Money Decisions in Real Life
Use everything from Unit 1 — pay rises, phone plans, family budgets, supermarket unit pricing and split bills — to make real money decisions. Then explain why "% of" and "% as" are different questions.
1. Word problems
Each problem requires you to pick the right move from the whole of Unit 1. Show your working — a final answer with no working only earns half marks.
1.1 — Pay rise. You earn $22.50 per hour. Your boss offers two options: (a) an 8% pay rise, OR (b) a flat $2/hour increase.
(i) Calculate the new hourly rate under each option.
(ii) Which option gives you the higher hourly rate? 3 marks
1.2 — Phone plan. A phone costs $880 inc-GST outright. Or you can pay $95 per month for 10 months.
(a) Total cost on the monthly plan?
(b) How much EXTRA does the monthly plan cost compared with paying outright?
(c) Express the extra as a percentage of the outright price. 3 marks
1.3 — Supermarket unit pricing. Two pasta packs on the shelf:
Pack A — 500 g for $4.00. Pack B — 750 g for $5.40.
(a) Find the price per kg for each pack.
(b) Which is the better buy? Justify with the numbers. 3 marks
1.4 — Restaurant split. A $315 inc-GST restaurant bill is split between 4 friends in the ratio 1 : 2 : 3 : 3 (because some had way more than others).
(a) How much does each friend pay?
(b) How much GST is included in the $315? 3 marks
1.5 — Family budget. A family's monthly grocery budget is $840, split in the ratio Food : Toiletries : Cleaning = 7 : 2 : 1. This month food prices go up 10%, cleaning prices fall 15%, toiletries stay the same.
(a) Find the original cost in each category.
(b) Find the new cost in each category after the price changes.
(c) Find the new total. Is it more or less than $840? By how much in dollars? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate is told: "A test mark of 18 out of 25 is the same as 18% as a percentage." They aren't sure. In your own words, explain (i) why "18 out of 25" is NOT 18%, (ii) what it actually is as a percentage, (iii) the difference between "find 18% of 25" and "express 18 out of 25 as a percentage". Use the phrase "% of vs % as" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pay rise
(i) Option (a): $22.50 × 1.08 = $24.30/hr. Option (b): $22.50 + $2 = $24.50/hr.
(ii) Option (b) is higher by $0.20/hr.
1.2 — Phone plan
(a) Monthly total = 10 × $95 = $950.
(b) Extra = $950 − $880 = $70.
(c) 70 / 880 × 100 ≈ 7.95% (about 8%).
1.3 — Pasta unit pricing
(a) Pack A: $4.00 ÷ 0.5 kg = $8.00/kg. Pack B: $5.40 ÷ 0.75 kg = $7.20/kg.
(b) Pack B is the better buy — it costs $0.80 less per kg.
1.4 — Restaurant split ($315 in 1 : 2 : 3 : 3)
(a) Total parts = 9. 1 part = $35. Shares: $35, $70, $105, $105. Check: 35 + 70 + 105 + 105 = $315 ✓.
(b) GST = $315 ÷ 11 ≈ $28.64.
1.5 — Family budget
(a) Total parts = 10. 1 part = $84. Food = $588; Toiletries = $168; Cleaning = $84.
(b) New: Food × 1.10 = $588 × 1.10 = $646.80; Toiletries unchanged = $168; Cleaning × 0.85 = $84 × 0.85 = $71.40.
(c) New total = $646.80 + $168 + $71.40 = $886.20. That's $886.20 − $840 = $46.20 MORE than the original — the family budget overruns by $46.20.
2.1 — Explain your thinking (sample response)
The classmate is mixing up "% OF" and "% AS". "18 out of 25" means 18 ÷ 25 = 0.72 = 72%, because the percentage tells us what fraction of the whole 25 the 18 is. It is NOT 18%.
The two questions are different: "find 18% OF 25" means take 0.18 × 25 = 4.5 (you START with 18% and apply it TO 25). "Express 18 OUT OF 25 AS a percentage" means divide 18 ÷ 25 = 0.72 = 72% (you START with the fraction 18/25 and CONVERT it to a percentage). The first uses a known percentage to find a part; the second uses a known part to find the percentage.
So the rule is: "% OF" multiplies by the percentage as a decimal, while "% AS" divides the part by the whole. Mixing up "% of vs % as" gives wildly different answers (here, 4.5 vs 72%).
Marking: 1 mark for the correct percentage (72%); 1 mark for the contrasting "% OF" calculation (4.5); 1 mark for explaining the directional difference between the two questions; 1 mark for using "% of vs % as" in a full-sentence rule.