Pack a moving truck full

Can you solve this question from the PISA exam?

Question 3: Pack a moving truck full

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How did your latest online order arrive on your doorstep so quickly? Well, mathematics plays a huge role in making that happen!

Mathematics is used to figure out the quickest routes for delivery, calculate the right amount of inventory to keep in stock, and even to design the packaging so your goods are protected during transit. Math ensures that warehouses, trucks, and delivery persons work together like a well-oiled machine, getting your orders to your doorstep efficiently and on time. So next time you’re wrestling with algebra or geometry, just remember—those equations and formulas are making sure you get your games, books, and gadgets just when you need them.

Question 3

Moving truck

Mara is moving her book collection with a moving truck, and is trying to figure out which size boxes to use to fill the truck's storage compartment completely.

Refer to the Interior Storage Compartment and Box Dimensions tables below:

**Interior Storage Compartment Dimensions**
Truck size	Length of floor	Width of floor	Height
A	4 meters	2 meters	2 meters

**Box Dimensions**
Box size	Length	Width	Height
Medium	0.5 meter	0.5 meter	0.5 meter
Large	0.5 meter	0.5 meter	0.75 meter

The truck rental company confirmed that truck A can be filled using only medium boxes so that the entire space in the storage compartment is used.

Mara claims that a medium box takes up 2/3 of the space of a large box, so she concludes that the number of large boxes that will fill truck A is 2/3 the number of medium boxes.

Which one of the following statements about Mara's conclusion is true?

(Choice A)
She is correct, because the height of a medium box is 2/3 the height of a large box.
(Choice B)
She is correct, because 3 medium boxes can always be fit into the same space as 2 large boxes.
(Choice C)
She is not correct, because none of the interior storage dimensions of truck A are multiples of 0.75, which is the height of a large box.
(Choice D)
She is not correct, because the height of a large box is 1.5 times the height of a medium box.

What skill does this question assess?

This question assesses reasoning. Reasoning mathematically, both deductively and inductively, involves evaluating situations, selecting strategies, drawing logical conclusions, developing and describing solutions, and recognising how those solutions can be applied.

This is a level 6 problem. At level 6, students can conceptualise, generalise and utilise information based on their investigations and modelling of complex problem situations, and can use their knowledge in relatively non-standard contexts. Students can apply insight, understanding, and a mastery of mathematical operations and relationships to develop new strategies for attacking novel situations.

As this question was not included in the main survey the % of students who got it right is not calculated.

Did you know?

For another fascinating moving company math conundrum, look up the "Travelling Salesman Problem," one of the most famous problems in computer science. It involves finding the shortest possible route that visits a set of locations and returns to the original departure point. Moving companies use solutions to this problem to optimize the routing and scheduling of their moving vans. This ensures not only timely service but also reduces operational costs and environmental impact. Solve this one and you’ll be in high demand from any company that moves goods or services around!

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Lovell2011
Posted 4 days ago. Direct link to Lovell2011's post “If I am moving from Flori...”
If I am moving from Florida to Oregon, using a car, how much is the gas, the measurement for the trip from one state to another?
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