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In a certain egg-processing plant, every egg must be inspected and is either accepted for processing or rejected. For

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by VJesus12 » Tue Sep 15, 2020 5:20 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

Answer: C

Source: Princeton Review
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Re: In a certain egg-processing plant, every egg must be inspected and is either accepted for processing or rejected. Fo

by deloitte247 » Sat Sep 19, 2020 11:54 am
Let the number of processed eggs per day = p
Let the number of accepted eggs per day = a
Let the number of rejected eggs per day = r
a = p - r


Given that for every 96 eggs accepted for processing 4 eggs were rejected
$$a:r=96:4$$
$$\frac{p-r}{r}=\frac{96}{4}$$
$$=\frac{p-r}{r}=\frac{24}{1}$$
$$p-r=24r$$
$$p=2r+r$$
$$p=25r$$
On a particular day 12 additional eggs were accepted but overall number of eggs inspected remains the same and a + 12 : r - 12 = 99 :1
$$\frac{p-r+12}{r-12}=\frac{99}{1}$$
$$p-r+12=99\left(r-12\right)$$
$$p-r=99r-1188-12\ where\ p=25r$$
$$25r-r-99r=-1200$$
$$\frac{-75r}{-75}=\frac{-1200}{-75}$$
$$r=16$$
$$p=25\cdot16=400eggs\ \ per\ day$$
$$Answer\ =\ C$$
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