The Student Room Group

Problem Solving

Tony makes ornaments which he sells in boxes that are cuboid in shape. The dimensions are either 5 cm × 5 cm × 12 cm or 5 cm × 6 cm × 10 cm. He needs to package them in larger boxes to send out to the shops that sell the ornaments for him and he wants to buy just one size of box. The box needs to hold exactly 6 ornaments of the same type (regardless of which type it is). The price of a box in cents is calculated by multiplying together the shortest two dimensions and then adding on the third. For example, a 2 cm × 3 cm × 4 cm box would cost 2 × 3 + 4 = 10 ¢. Tony wants to get the cheapest box possible. What will be the price of one box?
A $0.86
B $0.90
C $0.97
D $1.35
Answer is A
Reply 1
Can you spot how the two different item sizes can be arranged to give the same dimensions? The objects' dimensions have a fairly close relationship as they (must be) the same volume.

Then just think how you can arrange 6 to keep the smallest two sides as small as possible as you multiplly them together (the base area) and its cheaper to grow the longest side (the height).
(edited 12 months ago)
Reply 2
5 × 36 × 10,
5 × 10 +36 = 86 ¢ is that what you think?
(edited 12 months ago)
Reply 3
Original post by Ezcinr
5 × 36 × 10 = 86 ¢ is that what you think?


Yes, you can fit 6 of both objects in that volume and its the cheapest.

Note when youre posting questions, its good to post some form of attempt. A quick google seems to show its from a multichoice gce, but there is little advanced content in the question, so you should be able to have some form of attempt.
(edited 12 months ago)

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