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In a certain egg-processing plant, every egg must be

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In a certain egg-processing plant, every egg must be

by swerve » Tue Feb 26, 2019 10:14 am

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In a certain egg-processing plant, every egg must be inspected and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

The OA is C

Source: Princeton Review
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by Scott@TargetTestPrep » Fri Mar 01, 2019 9:39 am
swerve wrote:In a certain egg-processing plant, every egg must be inspected and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

The OA is C

Source: Princeton Review
We can create the ratio of the accepted eggs to the rejected eggs as 96x : 4x. Note that 100x eggs are processed every day. We can create the equation:

99/1 = (96x + 12)/(4x - 12)

99(4x - 12) = 96x + 12

99(x - 3) = 24x + 3

99x - 297 = 24x + 3

75x = 300

x = 4

Therefore, 100(4) = 400 eggs are processed every day.

Answer: C

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edited

by deloitte247 » Sat Mar 09, 2019 12:55 am
For original ratio, let total no of eggs = x
$$\frac{Total\ accepted}{Total\ rejected}=\frac{96x}{4x}$$
When additional 12 eggs are accepted, total number of eggs remains unchanged but ratio
$$=\frac{99}{1}$$
Therefore,
$$\frac{96x+12}{4x-12}=\frac{99}{1}$$
$$\left(96x+12\right)1=99\left(4x-12\right)$$
$$96x+12=396x-1188$$
$$12+1188=396x-96x$$
$$1200=300x$$
$$\frac{1200}{300}=\frac{300x}{300}$$
$$x=4$
$$96x:4x$$
$$=96x+4x$$
$$=96\left(4\right)+4\left(4\right)=$$
$$=384+16=400$$

$$answer\ is\ Option\ C$$
Last edited by deloitte247 on Sat Mar 09, 2019 2:36 am, edited 1 time in total.
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by deloitte247 » Sat Mar 09, 2019 2:06 am
For original ratio, let total no of eggs = x
$$\frac{Total\ accepted}{Total\ rejected}=\frac{96x}{4x}$$
When additional 12 eggs are accepted, total number of eggs remains unchanged but ratio
$$=\frac{99}{1}$$
Therefore,
$$\frac{96x+12}{4x-12}=\frac{99}{1}$$
$$\left(96x+12\right)1=99\left(4x-12\right)$$
$$96x+12=396x-1188$$
$$12+1188=396x-96x$$
$$1200=300x$$
$$\frac{1200}{300}=\frac{300x}{300}$$
$$x=4$
$$from\ original\ ratio\ of\ \ 96x:4x$$
$$Total\ no\ of\ processed\ eggs=96x+4x$$
$$=96\left(4\right)+4\left(4\right)=$$
$$=384+16=400$$
$$answer\ is\ Option\ C$$
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