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# A toy company expects the ratio of broken toys to the total number of

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Math Expert
Joined: 02 Sep 2009
Posts: 49364
A toy company expects the ratio of broken toys to the total number of  [#permalink]

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26 Nov 2017, 09:05
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00:00

Difficulty:

45% (medium)

Question Stats:

75% (01:48) correct 25% (02:01) wrong based on 56 sessions

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A toy company expects the ratio of broken toys to the total number of toys in all future shipments to be equal to the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 630,000 toys?

A. 20
B. 24
C. 29
D. 30
E. 33

Attachment:

2017-11-26_2003.png [ 11.81 KiB | Viewed 732 times ]

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Joined: 24 Nov 2016
Posts: 152
Re: A toy company expects the ratio of broken toys to the total number of  [#permalink]

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26 Nov 2017, 11:21
Bunuel wrote:

A toy company expects the ratio of broken toys to the total number of toys in all future shipments to be equal to the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 630,000 toys?

A. 20
B. 24
C. 29
D. 30
E. 33

Attachment:
2017-11-26_2003.png

So, all future shipments ratio of broken to total will be the same as the ratio of shipments combined above: (broken/total)*future = (20/420,000) * 630,000 = 30 (D)
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Re: A toy company expects the ratio of broken toys to the total number of  [#permalink]

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27 Nov 2017, 01:43
Because we are given the broken toys for each shipment 2+6+8+4 = 20
and the total # number of shipments = 50,000 + 135,000 + 165,000 + 70,000 = 420,000

the ratio is 20:420,000, simplifying it is becomes 1:21,000

Given the total number of shipment is 630,000 then to get how many defects given the ratio $$\frac{630,000}{21,000}= 30$$

Or we can do it this way also 10:210,000 and $$\frac{630,000}{210,000} = 3$$ so $$3*10 = 30$$
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Re: A toy company expects the ratio of broken toys to the total number of  [#permalink]

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29 Nov 2017, 10:54
Bunuel wrote:

A toy company expects the ratio of broken toys to the total number of toys in all future shipments to be equal to the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 630,000 toys?

A. 20
B. 24
C. 29
D. 30
E. 33

Attachment:
2017-11-26_2003.png

The ratio of broken toys to the total number of toys, which is calculated by dividing the sum of the broken toys in all shipments to the sum of the total number of toys in all shipments, is 20/420,000 = 1/21,000. We can let n = the number of defective toys in a shipment of 630,000 toys and create the following proportion:

1/21,000 = n/630,000

21,000n = 630,000

21n = 630

n = 30

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Re: A toy company expects the ratio of broken toys to the total number of &nbs [#permalink] 29 Nov 2017, 10:54
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