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I tried to write the following sentence as a proportion:

6 printers is to 24 computers as 2 printers is to 6 computers:

${6\,\,printers\over 2\,\,printers} = {24\,\,computers\over 6\,\,computers} $

But when I try to check if the statement is true, it is not. Therefore, it's not a proportion.

So what is the right way to write this?

Hosein Rahnama
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direprobs
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  • Since it's not mathematically true, what do you mean by "6 printers is to 24 computers as 2 printers is to 6 computers" ? – Hippalectryon Nov 11 '15 at 11:11
  • What we mean here is simply to write the sentence as a proportion ( two equal fractions), it doesn't necessarily mean it's logically true as printers and computers are separate entities. – direprobs Nov 11 '15 at 11:14
  • The problem isn't that printers and computers are separate entities, it's that $\frac{6}2\neq \frac{24}6$ – Hippalectryon Nov 11 '15 at 11:17

2 Answers2

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If you need $6$ printers to $24$ computers so $2$ printers for $\color{blue}8$ computers

$$\frac{24}{6}=\frac{8}{2}$$

$$\frac{24}{6}\color{red}\neq\frac{6}{2}$$

$\Longrightarrow1$ printer for $4$ computers, so if you have $6$ computers so you need $2$ printers

3SAT
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Let us check the first part of the statement. It says that, you need "6 Printers to 24 computers",which means you need 1 printer for 4 computers. For the second part, you have 6 computers with you and among these 6, the first 4 computers will have a total of one printer and the remaining 2 will have a total of one printer.

So in mathematics $$Computer/Printer=4$$ Now consider n, such that $n\equiv\ \text{#}computers\ (mod\ 4),\text{then }n\in \{0,1,2,3\}$, and if $n=0,$then we will assign n=4 (since 4$\in[0]$)

So our proportion in general will look like as following, $$\frac{\text{#}computer+(4-n)Computer}{\text# printer}$$ ie $$\frac{24Computer+(4-4)Computer}{6Printer}=\frac{6Computer+(4-2)Computer}{2Printer}=4$$

Community
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Ashwin Koodathil
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