Percentage Increase and Decrease

Find 10% first, then add it.

25% is one quarter. Find the quarter that is removed.

The question asks for the extra amount, not the new total.

Find 15% of 3.2, then add it, or use a multiplier.

The final amount is the original amount plus the increase.

Find the percentage that remains after the decrease.

1. 100\%-35\%=65\% remains.
2. 60\times0.65=39.

12.5% is one eighth, or use a multiplier of 0.875.

1. The reduction is 48\div8=6, or £6.
2. 48-6=42, so the new price is £42.

An 8% increase leaves you with 108% of the original number.

1. 600\times1.08=648.
2. The club has 648 members after the increase.

Find the percentage remaining, then write it as a decimal.

1. 100\%-7\%=93\%, so use 0.93.
2. 1400\times0.93=1302 litres remain.

Work out what percentage of the original remains.

1. 100\%-18\%=82\%.
2. The required calculation is 2500\times0.82. Multiplying by 0.18 finds the amount removed, not the amount left.

Apply the discount to the coat, then add delivery.

1. Discounted price: 64\times0.85=54.40.
2. Total cost: 54.40+4=58.40, or £58.40.

Apply the percentage change before converting kilograms to grams.

1. 2.4\times1.075=2.58 kg.
2. 2.58\times1000=2580 g.

Keep 88% of the price and round only the final result.

1. 17.99\times0.88=15.8312.
2. To the nearest penny, the new price is £15.83.

The 18 people are added after the percentage increase.

1. 240\times1.05=252 members after the increase.
2. 252+18=270 members in total.

Find the increase, then express it as a percentage of the original price.

1. Increase: 276-240=36, or £36.
2. 36\div240\times100=15.
3. The percentage increase is 15\%.

Each change uses the price at that stage.

1. After the decrease: 250\times0.80=200.
2. After the increase: 200\times1.15=230.
3. The final price is £230. The second percentage is based on £200, not £250.

Apply both changes to the correct starting amount at each stage.

1. 80\times1.15=92.
2. 92\times0.85=78.20, so the final price is £78.20.
3. 80-78.20=1.80, so it is £1.80 lower.
4. The rise adds £12, but the fall removes 92\times0.15=13.80, or £13.80. Equal percentages do not cancel when they use different starting prices.

Calculate both final totals before comparing the offers.

Part (a)

1. Shop A: 180\times0.80+6=144+6=150, or £150.
2. Shop B: 165\times0.90=148.50, or £148.50.
3. Shop B has the lower total price.

Part (b)

1. 150-148.50=1.50, so the difference is £1.50.

Find the ticket total, apply the percentage fee, then compare with the budget.

1. Tickets cost 36\times7.50=270, or £270.
2. Including the fee: 270\times1.20=324, or £324.
3. 324-320=4, so the group needs £4 more.

Find the increased price first. This is the starting amount for the later percentage decrease.

1. After the increase: 80\times1.25=100, so the price is £100.
2. The later reduction is 100-72=28, or £28.
3. 28\div100\times100=28, so the decrease from the increased price is 28\%.
4. Using £80 as the denominator would compare with the wrong stage of the problem.