Mathematics • Year 8 • Unit 1 • Lesson 5
Percentage Increase — Real World
Use the add and multiplier methods from Lesson 5 where increases actually happen: pay rises, rent, sports records, prices with GST, and growing audiences. Then explain your method in your own words.
1. Word problems
Each problem uses one of the percentage-increase methods from Lesson 5. Show your working and state which method you used.
1.1 — Pay rise. Your part-time job pays $22/hour. The boss offers everyone a 6% pay rise.
(a) Find the dollar increase per hour (the add-method intermediate step).
(b) Find your new hourly rate using the multiplier method.
(c) Check both methods give the same answer. 3 marks
1.2 — Rent goes up. A family's weekly rent is $480. The landlord increases it by 3.5%.
(a) Find the new weekly rent (use the multiplier method).
(b) Over a year (52 weeks), how much more do they pay because of this increase? 3 marks
1.3 — Concert audience. A small concert last year drew 850 people. This year ticket sales are up 22%.
(a) Estimate this year's audience using the multiplier method.
(b) Why does it make sense to round to the nearest whole person? 3 marks
1.4 — Price + GST. A $260 phone case has 10% GST added (GST is an increase by 10%).
(a) Write the multiplier for adding 10% GST.
(b) Use it to find the price you pay at the till (the "GST-inclusive" price). 3 marks
1.5 — Annual pay rises. A worker earns $50 000 per year. Their salary increases 7% every year.
(a) Find their salary after 1 year, after 2 years and after 3 years (apply the multiplier 1.07 once each time).
(b) After how many full years has their salary risen above $60 000? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate sees "a 15% pay rise" and says "Easy — multiplier is 0.15, so new pay = 0.15 × old pay." In your own words, explain (i) what mistake they have made, (ii) what the correct multiplier is for a 15% increase and WHY, and (iii) what 0.15 × old pay actually represents. Use the phrase "100% of the original" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pay rise
(a) Increase = 6% of $22 = 0.06 × 22 = $1.32/hour.
(b) Multiplier method: 1.06 × $22 = $23.32/hour.
(c) Add-method check: $22 + $1.32 = $23.32. ✓
1.2 — Rent goes up
(a) Multiplier = 1.035. New rent = 1.035 × $480 = $496.80/week.
(b) Weekly extra = $496.80 − $480 = $16.80. Yearly extra = 52 × $16.80 = $873.60 more per year.
1.3 — Concert audience
(a) Multiplier = 1.22. New audience ≈ 1.22 × 850 = 1037 people.
(b) Audience is a whole-number count of people — you can't have 0.5 of a person at a concert. So we round to the nearest whole number: 1037 people.
1.4 — Price + GST
(a) +10% multiplier = 1.10.
(b) Price at till = 1.10 × $260 = $286. (Check: GST itself = 10% of $260 = $26; $260 + $26 = $286. ✓)
1.5 — Annual pay rises
(a) After 1 year: 1.07 × 50 000 = $53 500. After 2 years: 1.07 × 53 500 = $57 245. After 3 years: 1.07 × 57 245 = $61 252.15.
(b) The salary crosses $60 000 between year 2 ($57 245) and year 3 ($61 252.15). So after 3 full years the salary is above $60 000.
2.1 — Explain your thinking (sample response)
My classmate has confused "the increase" with "the new total". A 15% pay rise means the new pay is the WHOLE old pay (100% of the original) PLUS an extra 15% of it — so the new pay is 115% of the old. The correct multiplier is 1 + 0.15 = 1.15, not 0.15. What 0.15 × old pay actually gives is just the dollar value of the increase by itself — for example, on a $20/hour wage, 0.15 × 20 = $3 is the rise, not the new pay. Add that $3 to the original $20 to get the new pay of $23 (which is exactly what 1.15 × 20 gives you in one step).
Marking: 1 mark for spotting that 0.15 gives only the increase; 1 mark for the correct multiplier 1.15; 1 mark for "100% of the original" + 15%; 1 mark for a worked example showing the difference clearly.