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Problem 369

Algebra Difficulty 2.5 Multiple choice CEMC Cayley · Canada · 2014

In a factory, Erika assembles 3 calculators in the same amount of time that Nick assembles 2 calculators. Also, Nick assembles 1 calculator in the same amount of time that Sam assembles 3 calculators. How many calculators in total can be assembled by Nick, Erika and Sam in the same amount of time as Erika assembles 9 calculators?

Pick one

Official solution

Erika assembling 9 calculators is the same as assembling three groups of 3 calculators.

Since Erika assembles 3 calculators in the same amount of time that Nick assembles 2 calculators, then he assembles three groups of 2 calculators (that is, 6 calculators) in this time.

Since Nick assembles 1 calculator in the same amount of time that Sam assembles 3 calculators, then Sam assembles 18 calculators while Nick assembles 6 calculators.

Thus, the three workers assemble $9+6+18=33$ calculators while Erika assembles 9 calculators.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.