Carl packs pens into boxes.
Each box holds 68 pens.
Carl has 980 pens and 14 boxes.
Does Carl have enough boxes to pack all the pens?
Show how you decide.
Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):
Let’s find out exactly how many pens Carl’s current supply of boxes can store altogether.
The total storage capacity is calculated by multiplying the number of boxes by the capacity per box: $14 \times 68 = 952$ pens.
Since he has 980 pens to pack, the capacity is too small, leaving 28 pens unpacked.
✅ Answer: No, because he can only pack 952 pens (or he needs 15 boxes)
(a) Bananas cost $\$1.20$ per kilogram and apples cost $\$2.25$ per bag.
Work out the total cost of 3.5 kg of bananas and 2 bags of apples.
(b) Students receive a 10% discount on their shopping.
Before the discount, the cost of a student’s shopping is $\$16.80$.
Work out the amount of the discount.
(c) The cost of a cabbage increases by 15%.
Calculate the new price if the original price is $\$1.80$.
(d) Some customers have their shopping delivered to their home.
The cost is $\$5$ plus $\$1.50$ for each kilometre travelled from the shop to their home.
(i) Show that the cost for a customer living 10km from the shop is $\$20$.
(ii) On the grid, draw a line to show the cost of having shopping delivered.
(e) A bottle of water costs $\$1.55$.
Suki has $\$20$.
Work out the maximum number of bottles Suki can buy and the change she receives.
(f) A farmer delivers eggs to the shop in trays of 50.
The eggs are then put into boxes of 12.
There are no eggs left in the trays and all of the egg boxes are full.
Work out the smallest possible number of eggs that the farmer delivers.
(g) The shop sells bottles of orange juice in three different sizes.
Work out which bottle is the best value.
Show how you decide.
(a) Ans: \$8.70
Bananas: $3.5 \times 1.20 = 4.20$
Apples: $2 \times 2.25 = 4.50$
Total: $4.20 + 4.50 = 8.70$
(b) Ans: \$1.68
Discount: $10\% \text{ of } 16.80 = 0.10 \times 16.80 = 1.68$
(c) Ans: \$2.07
Increase: $15\% \text{ of } 1.80 = 0.27$
New price: $1.80 + 0.27 = 2.07$
(d)(i) Ans: \$20
Delivery cost: $5 + (1.50 \times 10) = 5 + 15 = 20$
(d)(ii)
Line from (0,5) to (10,20) showing cost increases \$1.50 per km
(e) Ans: 12 bottles, \$1.40 change
Max bottles: $\left\lfloor \frac{20}{1.55} \right\rfloor = 12$
Change: $20 – (12 \times 1.55) = 1.40$
(f) Ans: 300 eggs
LCM of 50 and 12: $2^2 \times 3 \times 5^2 = 300$
(g) Ans: Bottle A
Price per litre:
A: $\frac{1.30}{0.5} = 2.60$
B: $\frac{3.20}{1.2} \approx 2.67$
C: $\frac{5.25}{2} = 2.625$
Bottle A is cheapest per litre.
