# Calculating a ratio from a ratio pattern

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?

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) – user2468 Aug 29 '12 at 4:17

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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Just added to my post – MistyD Aug 29 '12 at 4:18
Could you tell me how you got that. I guess I must be doing it wrong – MistyD Aug 29 '12 at 4:19
Figured it out.. But I still dont understand the combined meaning here – MistyD Aug 29 '12 at 4:21
@MistyD: With your addition, you are ignoring samples S1, S2, and S3. I took "S1,S2,S3 and S4 combined" to mean that you should consider the total of all of them as one sample. I still think that is the correct interpretation, but there are hazards translating English to Mathics. The fact that it divides easily supports this in a school problem setting. – Ross Millikan Aug 29 '12 at 4:22
Thanks for clearing that up – MistyD Aug 29 '12 at 4:27

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:

$$16000\div4=4000\;(1 shipment)$$ $$60000\div4000=15\;(shipment)$$

Hence, the right method is:

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

Or this is your preferred (algebra) method:

$$51000x=(60000\times17=1020000)$$

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