Problem 1

Hannah is having a party and has invited 14 friends (15 children including herself). She needs 3 cakes and 1 small bag of sweets for each child. Each packet contains 6 cakes, and each large packet of sweets contains 5 small packets.

a. How many packets of cakes do they need to buy?
  1. Total cakes needed: 15 children×3 cakes/child=45 cakes15 \text{ children} \times 3 \text{ cakes/child} = 45 \text{ cakes}
  2. Each packet contains 6 cakes: 45 cakes6 cakes/packet≈7.5 packets\frac{45 \text{ cakes}}{6 \text{ cakes/packet}} \approx 7.5 \text{ packets}
  3. They need to buy 8 packets (since they can't buy half packets).

Answer: 8 packets of cakes.

b. How many packets of sweets do they need to buy?
  1. Total small packets of sweets needed: 15 children×1 packet/child=15 small packets15 \text{ children} \times 1 \text{ packet/child} = 15 \text{ small packets}
  2. Each large packet contains 5 small packets: 15 small packets5 small packets/large packet=3 large packets\frac{15 \text{ small packets}}{5 \text{ small packets/large packet}} = 3 \text{ large packets}

Answer: 3 packets of sweets.

c. Total cost if cakes cost £2.99 each and sweets cost £2.89 each?
  1. Cost for cakes: 8 packets×£2.99=£23.928 \text{ packets} \times £2.99 = £23.92
  2. Cost for sweets: 3 packets×£2.89=£8.673 \text{ packets} \times £2.89 = £8.67
  3. Total cost: £23.92+£8.67=£32.59£23.92 + £8.67 = £32.59

Answer: £32.59

d. Change from £40 after spending the total amount?
  1. Amount given: £40
  2. Total spent: £32.59
  3. Change: £40−£32.59=£7.41

Answer: £7.41

Problem 2

John needs to buy pencils for his class of 34 children. He needs 2 pencils per child, and pencils come in packs of 6.

a. How many packs will he need? Will there be any pencils left over?
  1. Total pencils needed: 34 children×2 pencils/child=68 pencils34 \text{ children} \times 2 \text{ pencils/child} = 68 \text{ pencils}
  2. Each pack contains 6 pencils: 68 pencils6 pencils/pack≈11.33 packs\frac{68 \text{ pencils}}{6 \text{ pencils/pack}} \approx 11.33 \text{ packs}
  3. He needs to buy 12 packs (since he can't buy a fraction of a pack).
  4. Pencils in 12 packs: 12 packs×6 pencils/pack=72 pencils12 \text{ packs} \times 6 \text{ pencils/pack} = 72 \text{ pencils}
  5. Leftover pencils: 72 pencils−68 pencils needed=4 pencils72 \text{ pencils} - 68 \text{ pencils needed} = 4 \text{ pencils}

Answer: 12 packs needed; 4 pencils will be left over.

b. How much will John need to spend if a pack costs £1.99? How much change will he get from £30?
  1. Cost per pack: £1.99
  2. Total cost for 12 packs: 12×£1.99=£23.8812 \times £1.99 = £23.88
  3. Amount given: £30
  4. Change: £30−£23.88=£6.12£30 - £23.88 = £6.12

Answer: John needs to spend £23.88; he will get £6.12 as change.