Teach Me Maths

Best Buys

Question 12 marks

A pack of 8 pencils costs £2.40. Work out the cost per pencil, in pence.

Hint

Use one currency unit consistently.

Worked solution

A pack of 8 pencils costs £2.40. Work out the cost per pencil, in pence.

  1. £2.40 =240 pence.
  2. 240\div8=30 pence per pencil.

Question 22 marks

A 750 g bag of oats costs £1.80. Work out the cost per 100 g, in pence.

Hint

Scale the price to 100 g.

Worked solution

A 750 g bag of oats costs £1.80. Work out the cost per 100 g, in pence.

  1. 180\div750\times100=24 pence per 100 g.

Question 32 marks

A 600 ml bottle of juice costs £1.50. Work out its price per litre, in pounds.

Hint

One litre is 1000 ml.

Worked solution

A 600 ml bottle of juice costs £1.50. Work out its price per litre, in pounds.

  1. 1.50\div600\times1000=2.50 pounds per litre.

Question 44 marks

Pack A contains 6 pens for £2.10. Pack B contains 8 pens for £2.64.

Work out the cost of 24 pens using each pack size.

(a)

Using only pack A, in pounds.

2 marks

(b)

Using only pack B, in pounds.

2 marks

Hint

Compare the same total number of pens.

Worked solution

Pack A contains 6 pens for £2.10. Pack B contains 8 pens for £2.64.

Work out the cost of 24 pens using each pack size.

Part (a)

Using only pack A, in pounds.

  1. 24\div6=4 packs; 4\times2.10=8.40 pounds.

Part (b)

Using only pack B, in pounds.

  1. 24\div8=3 packs; 3\times2.64=7.92 pounds.

Question 52 marks

A 400 g bag of rice costs £2. A 500 g bag of rice also costs £2.

For each £1 spent, how many more grams of rice do you get with the 500 g bag?

Hint

Work out how many grams of each bag you get for £1.

Worked solution

A 400 g bag of rice costs £2. A 500 g bag of rice also costs £2.

For each £1 spent, how many more grams of rice do you get with the 500 g bag?

  1. 500 g bag: 500\div2=250 g for each £1.
  2. 400 g bag: 400\div2=200 g for each £1.
  3. Difference: 250-200=50 g.

Question 62 marks

Two shops each sell packs of 10 envelopes. Shop A charges £1.90 and shop B charges £1.70.

How many pence per envelope are saved by buying from B?

Hint

The pack sizes are equal.

Worked solution

Two shops each sell packs of 10 envelopes. Shop A charges £1.90 and shop B charges £1.70.

How many pence per envelope are saved by buying from B?

  1. Pack saving: 190-170=20 pence.
  2. Saving per envelope: 20\div10=2 pence.

Question 73 marks

Battery packs are sold as follows.

  • A:4 batteries for £1.40
  • B:6 batteries for £1.92
  • C:10 batteries for £3.40

Work out the cost per battery for each pack, in pence.

(a)

Pack A.

1 mark

(b)

Pack B.

1 mark

(c)

Pack C.

1 mark

Hint

Divide each pack price by its own number of batteries.

Worked solution

Battery packs are sold as follows.

  • A:4 batteries for £1.40
  • B:6 batteries for £1.92
  • C:10 batteries for £3.40

Work out the cost per battery for each pack, in pence.

Part (a)

Pack A.

  1. 140\div4=35 pence.

Part (b)

Pack B.

  1. 192\div6=32 pence.

Part (c)

Pack C.

  1. 340\div10=34 pence.
  2. B has the lowest unit price.

Question 81 mark

A 300 g pack costs £1.20 and a 500 g pack costs £2. Which statement is correct?

Hint

Compare equal quantities.

Worked solution

A 300 g pack costs £1.20 and a 500 g pack costs £2. Which statement is correct?

  1. The 300 g pack is better value.
  2. The 500 g pack is better value.
  3. Both have the same cost per 100 g.
  1. 120\div3=40 pence per 100 g.
  2. 200\div5=40 pence per 100 g, so the values are equal.

Question 92 marks

One bottle costs £1.40. An offer gives 2 bottles for £2.50. Work out the saving when buying 6 bottles using the offer, in pounds.

Hint

Compare the ordinary cost with three offer pairs.

Worked solution

One bottle costs £1.40. An offer gives 2 bottles for £2.50. Work out the saving when buying 6 bottles using the offer, in pounds.

  1. Ordinary cost: 6\times1.40=8.40 pounds.
  2. Offer cost: 3\times2.50=7.50 pounds.
  3. Saving: £0.90.

Question 102 marks

Shop A sells 4 rolls for £1.80. Shop B sells 6 rolls for 240 pence.

How many pence per roll are saved at shop B?

Hint

Convert both prices to pence.

Worked solution

Shop A sells 4 rolls for £1.80. Shop B sells 6 rolls for 240 pence.

How many pence per roll are saved at shop B?

  1. A: 180\div4=45 pence per roll.
  2. B: 240\div6=40 pence per roll.
  3. Saving: 45-40=5 pence.

Question 113 marks

Shop A sells a 2 kg bag of flour for £3.20 with 25% off. Shop B sells 500 g bags for 65 p each.

How much is saved by buying 2 kg at A rather than B, in pounds?

Hint

Compare the discounted price with four small bags.

Worked solution

Shop A sells a 2 kg bag of flour for £3.20 with 25% off. Shop B sells 500 g bags for 65 p each.

How much is saved by buying 2 kg at A rather than B, in pounds?

  1. A: 3.20\times0.75=2.40 pounds.
  2. B: 4\times0.65=2.60 pounds.
  3. Saving: £0.20.

Question 124 marks

Cereal A normally contains 400 g for £2.40 and now has 25% extra cereal for the same price. Cereal B contains 500 g for £2.60 with 10% off.

Work out each cost per 100 g, in pence.

(a)

Cereal A.

2 marks

(b)

Cereal B.

2 marks

Hint

Work out the new size or price before comparing.

Worked solution

Cereal A normally contains 400 g for £2.40 and now has 25% extra cereal for the same price. Cereal B contains 500 g for £2.60 with 10% off.

Work out each cost per 100 g, in pence.

Part (a)

Cereal A.

  1. A contains 400\times1.25=500 g.
  2. 240\div5=48 pence per 100 g.

Part (b)

Cereal B.

  1. B costs 260\times0.90=234 pence.
  2. 234\div5=46.8 pence per 100 g.

Question 134 marks

Shop A sells identical tins at 80 p each, with 3 tins for the price of 2. Shop B sells the same tins at 90 p each, with every second tin half price.

Work out the difference between the costs of 6 tins, in pounds.

Hint

Group the tins according to each offer.

Worked solution

Shop A sells identical tins at 80 p each, with 3 tins for the price of 2. Shop B sells the same tins at 90 p each, with every second tin half price.

Work out the difference between the costs of 6 tins, in pounds.

  1. A: two groups of 3 cost 2\times(2\times0.80)=3.20 pounds.
  2. B: three pairs cost 3\times(0.90+0.45)=4.05 pounds.
  3. Difference: £0.85.

Question 143 marks

A shop sells notebooks for £1.80 each or 3 for £4.50. An offer can be used more than once.

Work out the lowest cost of buying exactly 7 notebooks, in pounds.

Hint

Use complete offer groups and pay for any remaining notebook.

Worked solution

A shop sells notebooks for £1.80 each or 3 for £4.50. An offer can be used more than once.

Work out the lowest cost of buying exactly 7 notebooks, in pounds.

  1. Two groups of 3 cost £9. One further notebook costs £1.80.
  2. Total: £10.80. Replacing an offer group by three single notebooks would cost more.

Question 153 marks

Shop A sells ink cartridges for £8 each plus £3 delivery per order. Shop B sells the same cartridges for £8.70 each with no delivery charge.

Work out how much cheaper B is for an order of 4 cartridges, in pounds.

Hint

Delivery is charged once per order.

Worked solution

Shop A sells ink cartridges for £8 each plus £3 delivery per order. Shop B sells the same cartridges for £8.70 each with no delivery charge.

Work out how much cheaper B is for an order of 4 cartridges, in pounds.

  1. A: 4\times8+3=35 pounds.
  2. B: 4\times8.70=34.80 pounds.
  3. B is £0.20 cheaper.

Question 16Challenge4 marks

A small pack contains 4 markers and costs £2.40. A large pack contains 10 markers and costs £5.

Sam needs at least 12 markers. Packs cannot be split. Work out the least amount he must spend, in pounds.

Hint

The best unit price may not give the lowest total for the required number.

Worked solution

A small pack contains 4 markers and costs £2.40. A large pack contains 10 markers and costs £5.

Sam needs at least 12 markers. Packs cannot be split. Work out the least amount he must spend, in pounds.

  1. Three small packs give 12 markers for £7.20.
  2. One large and one small give 14 for £7.40. Two large give 20 for £10.
  3. The least cost is £7.20.

Question 17Challenge4 marks

A supermarket in the UK sells a 3.5 pint bottle of milk for £1.40. A supermarket in Spain sells a 1.5 litre bottle of milk for 1.38 euros.

1 litre =1.75 pints

£1 =1.15 euros

(a)

In which country is the milk better value for money?

1 mark

(b)

Work out the difference between the costs of 1 litre of milk in the two countries, in pence.

3 marks

Hint

Compare the cost of the same amount of milk in the same currency.

Worked solution

A supermarket in the UK sells a 3.5 pint bottle of milk for £1.40. A supermarket in Spain sells a 1.5 litre bottle of milk for 1.38 euros.

1 litre =1.75 pints

£1 =1.15 euros

Part (a)

In which country is the milk better value for money?

  1. The UK
  2. Spain
  1. UK: 3.5\div1.75=2 litres for £1.40, so £0.70 for 1 litre.
  2. Spain: 1.38\div1.15=1.20 pounds for 1.5 litres, so 1.20\div1.5=0.80 pounds for 1 litre.
  3. £0.70 is less than £0.80, so the milk in the UK is better value.

Part (b)

Work out the difference between the costs of 1 litre of milk in the two countries, in pence.

  1. 1 litre costs 70 pence in the UK and 80 pence in Spain.
  2. Difference: 80-70=10 pence.

Question 18Challenge4 marks

Shop A sells a set of 12 towels for £36, with 25% off. Shop B sells the same set for £32 and gives £4 off the set.

How many pence per towel are saved by choosing the cheaper shop? Give your answer to 1 decimal place.

Hint

Apply both offers, then compare the saving per towel.

Worked solution

Shop A sells a set of 12 towels for £36, with 25% off. Shop B sells the same set for £32 and gives £4 off the set.

How many pence per towel are saved by choosing the cheaper shop? Give your answer to 1 decimal place.

  1. A: 36\times0.75=27 pounds. B: 32-4=28 pounds.
  2. Saving for 12 towels is £1, or 100 p.
  3. 100\div12=8.333\ldots pence per towel, rounding to 8.3 p.

Question 19Challenge4 marks

A UK shop sells 750 g of coffee for £12. A French shop sells 1 kg of the same coffee for 18 euros.

The exchange rate is £1 =1.25 euros. There are no other charges.

How many pounds per kilogram are saved at the French shop?

Hint

Use the same mass and currency for comparison.

Worked solution

A UK shop sells 750 g of coffee for £12. A French shop sells 1 kg of the same coffee for 18 euros.

The exchange rate is £1 =1.25 euros. There are no other charges.

How many pounds per kilogram are saved at the French shop?

  1. UK price per kg: 12\div0.75=16 pounds.
  2. French price per kg: 18\div1.25=14.40 pounds.
  3. Saving: £1.60 per kg.

Question 20Challenge4 marks

A supplier sells notebooks in packs of 5 for £3 and in packs of 8 for £4.60. Delivery costs £3.50 for an order under £12. Delivery is free for an order of £12 or more.

A teacher needs 16 notebooks. She will buy packs of one size only.

Work out the lowest total cost, including delivery, in pounds.

Hint

Work out the number of packs needed for each pack size, then check whether delivery must be paid.

Worked solution

A supplier sells notebooks in packs of 5 for £3 and in packs of 8 for £4.60. Delivery costs £3.50 for an order under £12. Delivery is free for an order of £12 or more.

A teacher needs 16 notebooks. She will buy packs of one size only.

Work out the lowest total cost, including delivery, in pounds.

  1. Packs of 5: 3 packs give only 15 notebooks, so she needs 4 packs. Cost: 4\times3=12 pounds. This is £12 or more, so delivery is free: £12.
  2. Packs of 8: 2 packs give 16 notebooks. Cost: 2\times4.60=9.20 pounds. This is under £12, so add £3.50: 9.20+3.50=12.70 pounds.
  3. The lowest total cost is £12, using packs of 5.

More on this topic: Best Buys worksheet with full solutions

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