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Calculator 3 marks
Orange juice is sold in two sizes.
A 200 ml carton of orange juice costs £1.10.
A 700 ml carton of orange juice costs £3.15.
Which size is better value for money? You must show your working.
Show answer
The 700 ml carton is better value for money.Work out what 100 ml costs in each size.
The 200 ml carton holds 2 lots of 100 ml:
\(£1.10 \div 2 = £0.55\) for 100 ml
The 700 ml carton holds 7 lots of 100 ml:
\(£3.15 \div 7 = £0.45\) for 100 ml
£0.45 is less than £0.55, so the 700 ml carton is better value for money.
- M1a price per unit, or the price of equal amounts, for one size
- M1the same for the other size
- A1the 700 ml carton
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Calculator 3 marks
Rice is sold in two sizes.
A bag holding \(800\) g costs \(£4\).
A bag holding \(200\) g costs \(£2\).
(a)Work out how many g of rice you get for \(£1\) from the \(800\) g bag.
(b)Work out how many g of rice you get for \(£1\) from the \(200\) g bag.
(c)State which bag is better value for money.
Show answer
(a) \(200\ \text{g}\)
(b) \(100\ \text{g}\)
(c) The 800 g bagDivide the amount by the number of pounds it costs.
\(800 \div 4 = 200\) g for \(£1\)
\(200 \div 2 = 100\) g for \(£1\)
Comparing this way round, more is better: the bag that gives you the most for your pound is the better buy.
\(200\) g for \(£1\) against \(100\) g for \(£1\), so the \(800\) g bag is better value.
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Calculator 4 marks
A shop sells bars of soap.
One bar of soap costs \(50\)p.
A pack of \(8\) bars of soap costs \(£3.45\).
(a)Find the cost of \(8\) single bars of soap.
(b)Work out how much is saved by buying the pack instead.
(c)Isla buys \(4\) packs.
Work out how much she pays, and how many bars of soap she gets.
Show answer
(a) \(£4.00\)
(b) \(£0.55\)
(c) £13.80 for 32 bars of soap\(8 \times 50 = 400\) pence
\(400\text{p} = £4.00\)
\(£4.00 - £3.45 = £0.55\)
\(4 \times £3.45 = £13.80\)
\(4 \times 8 = 32\) bars of soap
- (c) B1cost £13.80
- (c) B1number of bars of soap \(32\)
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Calculator 5 marks
A shop sells two brands of battery.
The figure shows the number of batteries in one pack of each brand, and the price of one pack.
One Zapp battery powers a toy for 3 hours.
One Voltex battery powers the same toy for \(5\frac{1}{4}\) hours.
Which brand is better value? You must show your working.
Show answer
Voltex is better value. Zapp costs 54p per battery and 18p per hour of use; Voltex costs 84p per battery and 16p per hour of use.Read the number of batteries in each pack from the figure, then work out the cost of one battery.
Zapp: £2.70 is 270p, so \(270 \div 5 = 54\), which is 54p per battery.
Voltex: £7.56 is 756p, so \(756 \div 9 = 84\), which is 84p per battery.
Now find the cost of one hour of use.
Zapp: \(54 \div 3 = 18\), which is 18p per hour.
Voltex: \(5\frac{1}{4}\) hours is \(\frac{ 21 }{ 4 }\) hours, so \(84 \div \frac{ 21 }{ 4 } = 84 \times \frac{ 4 }{ 21 } = 16\), which is 16p per hour.
16p is less than 18p, so Voltex is better value.
- M1cost per battery for Zapp, \(270 \div 5 = 54\)p (or hours in one pack, \(5 \times 3 = 15\))
- M1cost per battery for Voltex, \(756 \div 9 = 84\)p (or hours in one pack, \(9 \times 5\frac{1}{4} = 47.25\))
- M1cost per hour for Zapp, 18p (or the equivalent hours per pound)
- M1cost per hour for Voltex, 16p (or the equivalent hours per pound)
- A1Voltex, comparing 16p with 18p per hour
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Calculator 3 marks
Apple juice is sold in two sizes.
A carton holding 600 ml costs £1.20.
A carton holding 1.25 litres costs £3.00.
Which carton is better value for money? You must show your working.
Show answer
The 600 ml carton: £2.00 per litre against £2.40 per litre.The sizes are in different units, so change them to the same unit first.
\(600\) ml \(= 600 \div 1000 = 0.6\) litres
One carton now holds 0.6 litres and the other holds 1.25 litres. Work out the price of \(1\) litre for each carton.
The 0.6 litres carton: \(£1.20 \div 0.6 = £2.00\) per litre
The 1.25 litres carton: \(£3.00 \div 1.25 = £2.40\) per litre
£2.00 per litre is less than £2.40 per litre, so the 600 ml carton is better value for money.
- M1both sizes in the same unit, e.g. 600 ml = 0.6 litres
- M1both unit prices in the same unit, £2.00 and £2.40 per litre (or equivalent)
- A1the 600 ml carton
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Calculator 3 marks
Kofi works for \(21\) hours and is paid \(£275.94\).
Hannah works for \(36\) hours and is paid \(£468.36\).
Kofi is paid more per hour than Hannah.
Work out how much more per hour Kofi is paid than Hannah.
Show answer
\(£0.13\)Divide each person's pay by their hours to find the pay for one hour.
Kofi: \(£275.94 \div 21 = £13.14\) per hour
Hannah: \(£468.36 \div 36 = £13.01\) per hour
Kofi is paid more per hour, so subtract the smaller rate from the larger:
\(£13.14 - £13.01 = £0.13\)
Kofi is paid \(£0.13\) more per hour.
- M1hourly rate for Kofi: \(£275.94 \div 21 = £13.14\)
- M1hourly rate for Hannah: \(£468.36 \div 36 = £13.01\)
- A1difference in the rates \(£0.13\)
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Calculator 4 marks
Batteries are sold in three different packs.
Pack Price 5 batteries £1.50 10 batteries £5.50 15 batteries £6.75 Which pack is the best value for money? You must show your working.
Show answer
The pack of 5 batteries is the best value for money.Work out the cost of one battery in each pack.
Pack of 5: \(£1.50 \div 5 = £0.30\)
Pack of 10: \(£5.50 \div 10 = £0.55\)
Pack of 15: \(£6.75 \div 15 = £0.45\)
£0.30 is the lowest cost for one battery, so the pack of 5 batteries is the best value for money.
- M1a price per item for one pack
- M1a price per item for the other two packs
- A1all three prices per item correct
- A1the pack of 5 batteries
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Calculator 4 marksA shop sells photo frames at £4.40 each. The shop has two offers on photo frames.
Offer A: buy 3, get 1 free
Offer B: 30% off when you buy 4
Idris wants to buy 4 photo frames.(a)Work out how much he pays using Offer A.
(b)Work out how much he pays using Offer B.
(c)Write down which offer is cheaper for 4 photo frames.
Show answer
(a) \(£13.20\)
(b) \(£12.32\)
(c) Offer B, by £0.88Offer A gives the fourth photo frame free, so he pays for 3.
\(3 \times £4.40 = £13.20\)
Four at full price would be
\(4 \times £4.40 = £17.60\)
Offer B takes 30% off that.
\(30\% \text{ of } £17.60 = £5.28\)
\(£17.60 - £5.28 = £12.32\)
\(£13.20\) against \(£12.32\), so Offer B is cheaper, by \(£0.88\).
- (b) M1\(30\%\) of £17.60 \(= £5.28\)
- (b) A1cost £12.32
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Calculator 4 marks
Amara wants to buy 4 bath towels.
Shop A sells bath towels at £6.30 each and charges £7.00 for delivery on any order.
Shop B sells bath towels at £8.20 each with free delivery.
Which shop is cheaper for 4 bath towels? You must show your working.
Show answer
Shop AShop A charges for the bath towels and then for the delivery.
\(4 \times £6.30 = £25.20\)
\(£25.20 + £7.00 = £32.20\)
Shop B charges for the bath towels only.
\(4 \times £8.20 = £32.80\)
£32.20 is less than £32.80, so shop A is cheaper.
- M1cost of the bath towels at Shop A, \(4 \times £6.30 = £25.20\)
- M1add delivery, \(£25.20 + £7.00 = £32.20\)
- M1total at Shop B, \(4 \times £8.20 = £32.80\)
- A1Shop A, comparing £32.20 with £32.80
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Calculator 4 marks
A pack of 12 cans of lemonade costs £6.30. Each can holds 250 ml.
A bottle of lemonade holds 1.5 litres and costs £3.90.
Which is better value for money? You must show your working.
Show answer
The packThe pack and the bottle hold different amounts, so the two prices cannot be compared directly. Work out what one litre costs each way.
The pack holds \(12 \times 250 = 3000\) ml, which is 3 litres.
\(£6.30 \div 3 = £2.10\) for one litre
The bottle holds 1.5 litres.
\(£3.90 \div 1.5 = £2.60\) for one litre
£2.10 is less than £2.60, so the pack is better value for money.
- M1pack size in litres, \(12 \times 250 = 3000\) ml \(= 3\) litres
- M1price per litre for the pack, \(£6.30 \div 3 = £2.10\)
- M1price per litre for the bottle, \(£3.90 \div 1.5 = £2.60\)
- A1the pack, comparing £2.10 with £2.60