Year 8 Mathematics | Victorian Curriculum 2.0
Percentages in context
Topic 05 | Number & Algebra | Answer key

Year 8 core - answers

Fluency

Increase and decrease

    1. 100100.
    2. $132. Method: 150×0.88150 \times 0.88.
    3. $102. Method: 85×1.2085 \times 1.20.
    4. 235235. Method: 250×0.94250 \times 0.94.
    5. $68. Method: 85×0.8085 \times 0.80.
    6. $129.60. Method: 120×1.08120 \times 1.08.
Fluency

Reverse problems

    1. $40. Method: 461.15\dfrac{46}{1.15}.
    2. $48. Method: 360.75\dfrac{36}{0.75}.
    3. $60,000. Method: 630001.05\dfrac{63000}{1.05}.
    4. 10 00010\,000. Method: 92000.92\dfrac{9200}{0.92}.
Fluency

Profit, loss, GST

    1. 25%25\% profit. Method: profit $15; 1560×100\dfrac{15}{60} \times 100.
    2. 15%15\% loss. Method: loss $30; 30200×100\dfrac{30}{200} \times 100.
    3. $53.90. Method: 49×1.1049 \times 1.10.
    4. $7. Method: 7711\dfrac{77}{11}.
    5. $50. Method: 551.10\dfrac{55}{1.10}.
Reasoning

Percentage error & explain

    1. 2.5%2.5\%. Method: ∣12.3−12∣12×100\dfrac{|12.3 - 12|}{12} \times 100.
    2. 25%25\% off. Method: discount $25; 25100×100\dfrac{25}{100} \times 100.
    3. Not true. Example starting $100: 100→130→91100 \to 130 \to 91, below the original.
    4. They are different. Two successive cuts: 100→80→72100 \to 80 \to 72 (net 28%28\% off). A single 30%30\% off gives 7070. Successive cuts are less generous than the nominal sum.
Problem solving

Real contexts

    1. $1309. Method: discount: 1400×0.85=11901400 \times 0.85 = 1190; add GST: 1190×1.10=13091190 \times 1.10 = 1309.
    2. $857.36 per week. Method: 800×1.04×1.03800 \times 1.04 \times 1.03.
    3. 12%12\%. Method: rise 15001500; 150012500×100\dfrac{1500}{12500} \times 100.
    4. $99. Method: 108911\dfrac{1089}{11}.
    5. 500500 g jar is cheaper per gram. 500500 g: 1.101.10 c/g. 750750 g: 1.0271.027 c/g. Actually the 750750 g is cheaper by about 6.7%6.7\% per gram (1.10−1.0271.10×100\dfrac{1.10 - 1.027}{1.10} \times 100).

Challenge - answers

Reasoning

Harder reasoning

    1. Start AA. After rise: A(1+r/100)A(1 + r/100). After fall of r%r\%: A(1+r/100)(1−r/100)=A(1−r2/10000)A(1 + r/100)(1 - r/100) = A(1 - r^2/10000). This is less than AA for r≠0r \ne 0. Net change: −r2/100%-r^2/100 \% (a decrease).
    2. Final is below cost. Starting from cost CC: mark-up gives 1.25C1.25 C; 20%20\% off that gives 0.80×1.25C=1.00C0.80 \times 1.25 C = 1.00 C. So the final price equals cost - no profit.
    3. 12.5%12.5\%. Method: ∣27−24∣24×100\dfrac{|27 - 24|}{24} \times 100.
    4. $595.51. Method: 500×1.063=500×1.191016=595.508500 \times 1.06^3 = 500 \times 1.191016 = 595.508.
Year 8 Mathematics study companion | Answer key