Hannah is having a party and has invited 14 friends (15 children including herself).

a. How many packets of cakes do they need to buy?

• Each child needs 3 cakes.
• Total number of cakes needed = 15 children * 3 cakes/child = 45 cakes.
• There are 6 cakes in a packet.
• Number of packets of cakes = 45 cakes / 6 cakes per packet = 7.5 packets.
• Since they can't buy half a packet, they need to buy 8 packets of cakes.

b. If there are 5 small packets of sweets in one large packet; how many packets of sweets do they need to buy?

• Each child needs 1 small packet of sweets.
• Total number of small packets needed = 15 children * 1 packet/child = 15 small packets.
• There are 5 small packets in one large packet.
• Number of large packets of sweets = 15 small packets / 5 small packets per large packet = 3 large packets.

c. If the packets of cakes cost £2.99 each and the packets of sweets cost £2.89, how much will they spend?

• Cost of cakes = 8 packets * £2.99/packet = £23.92.
• Cost of sweets = 3 packets * £2.89/packet = £8.67.
• Total cost = £23.92 + £8.67 = £32.59.

d. Hannah’s mum pays with two £20 notes; what change does she get?

• Total amount paid = 2 * £20 = £40.
• Change = £40 - £32.59 = £7.41.

John has been asked to buy some new pencils for his class of 34 children.

a. If the pencils come in packs of 6; how many packs will he need? Will there be any pencils left over?

• Each child needs 2 pencils.
• Total number of pencils needed = 34 children * 2 pencils/child = 68 pencils.
• Pencils per pack = 6.
• Number of packs = 68 pencils / 6 pencils per pack ≈ 11.33 packs.
• Since they can't buy a fraction of a pack, they need 12 packs.
• Number of pencils in 12 packs = 12 packs * 6 pencils/pack = 72 pencils.
• Leftover pencils = 72 pencils - 68 pencils needed = 4 pencils.

b. If a pack costs £1.99; how much will John need to spend? If John is given £30 to spend; how much change will he get?

• Cost of 12 packs = 12 packs * £1.99/pack = £23.88.
• Amount given = £30.
• Change = £30 - £23.88 = £6.12.