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I am having difficulty with the following problem

A computer chip manufacturer expects the ratio of number of defective chips to the number of chips in all future shipments to equal corresponding ratio for shipments S1,S2,S3 and S4 combined as shown in the table. What is the number of defective chips for a shipment of $60,000$ chips. (Ans=20). Any suggestions on how I could solve this problem?

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I believe I am suppose to find S5 for $60,000$ which follows the ratio pattern. So I am doing the following

$16000$x =$60,000\times4$ so I get x=$15$ which is incorrect

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    Oh, I didn't notice "combined". Ignore my previous comment. (edit: also, Google reveals it's a GMAT preparation question or something. E.g. see [discussion here](http://gmatclub.com/forum/a-computer-chip-manufacturer-expects-the-ratio-of-the-number-103607.html))2012-08-29

2 Answers 2

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There are a total of 51,000 chips in the four samples with 17 defective. The defective rate is therefore 1 per 3,000.

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    Thanks for clearing that up2012-08-29
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Base on the table alone, there are no ways to solve this.

However,

the number of chips in all future shipments to equal corresponding ratio for shipments S1,S2,S3 and S4 combined as shown in the table.

Meaning S20 is related to S1, S2, S3 and S4.

If I want to calculate 1 defective coin, I cannot make use of 1 shipment only.

Thus, this is wrong:

\begin{equation} 16000\div4=4000\;(1 shipment) \end{equation} \begin{equation} 60000\div4000=15\;(shipment) \end{equation}

Hence, the right method is:

\begin{equation} 2+5+6+4=17\;(total\,defective\,chips\,in\,4\,shipments) \end{equation} \begin{equation} 5000+12000+18000+16000=51000\;(total\,chips\,in\,the\,4\,shipments) \end{equation} \begin{equation} 51000\div17=3000\;(total\,chips\,per\,shipment) \end{equation} \begin{equation} 60000\div3000=20 \end{equation}

Or this is your preferred (algebra) method:

\begin{equation} 51000x=(60000\times17=1020000) \end{equation}