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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?

  1. $30$
  2. $24$
  3. $27$
  4. $33$
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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.
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E:N:S

3:2

   1:3

E:N:S=3:2:6=9:6:18

9+6+18=33

 

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