Question

Packages of 500 sheets of printer paper 216 mm × 279 mm × 45 mm are available packaged in cases 216 mm × 279 mm × 270 mm. Jacinta needs to order 7,000 sheets for a small office but can only order full cases. How many cases should they order, and why?

Answer 1

It is logical to get three cases

Explanation:

The length and the width of the 500 sheet paper are 216 and 279 mm, respectively, which means that the height for the 500 sheet paper is 45 mm, and for the package, it is 270 mm. This means that 6 (270/45) 500 sheet papers can fit, which is 3000 individual papers. She needs 7000, and since she can only get 6000 from each full case (and can only get it from a full case) she needs to get 3 cases; because if she only gets 2, she can't get any extra, but if she gets three, she gets extra but heeds to her limit. So it is logical to get three cases.

Answer 2

3 cases

Explanation:

You want to know the number of cases of printer paper that should be ordered to fill a need for 7000 sheets when there are 500 sheets per 45 mm package in a 270 mm case.

Case size

Each package is 45 mm thick, and the case is 270 mm thick. The case will hold ...

(270 mm/case) / (45 mm/package) = 270/45 packages/case

= 6 packages/case

Need

The number of packages needed is ...

(7000 sheets) / (500 shees/package) = 7000/500 packages

= 14 packages

Then the number of cases needed is ...

(14 packages) / (6 packages/case) = 14/6 cases = 2 1/3 cases

If only whole cases can be ordered, 3 cases should be ordered to fill the need.

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Additional comment

We notice that the 216 mm×279 mm footprint of a package is the same as that for a case, so we only need to be concerned with the thickness of the package and the case.