Question

A grocery store worker is checking for broken eggs in

egg cartons. Each carton of eggs contains 12 eggs. He checks 4 cartons and finds 8 broken eggs. Based on these results. what can the worker predict about the rest of the cartons of eggs?

A) 6 cartons of eggs will contain 4 more broken eggs than 4 cartons.
B) 8 cartons of eggs will contain 12 more broken eggs than 4 cartons.
C) 10 cartons of eggs will contain 8 more broken eggs than 4 cartons.
D) 12 cartons of eggs will contain 14 more broken eggs than 4 cartons.

Answer 1

10 cartons of eggs will contain 8 more broken eggs than 4 cartons if a grocery store worker is checking for broken egg cartons. Each carton of eggs contains 12 eggs. He checks 4 cartons and finds 8 broken eggs.

Assuming that the proportion of broken eggs in the sampled cartons is representative of the entire batch of cartons, the worker can use this information to predict the number of broken eggs in the rest of the cartons.

The worker checked 4 cartons of eggs, each with 12 eggs, for a total of 4 x 12 = 48 eggs. Out of these 48 eggs, 8 were found to be broken.

To estimate the number of broken eggs in the rest of the cartons, the worker can use proportionality. The proportion of broken eggs in the sample is 8/48 = 1/6. Therefore, the worker can predict that out of the marginal cost remaining cartons of eggs, 1/6 of the eggs will be broken.

The closest option is C, which predicts that there will be 16 broken eggs in 10 cartons, which is 8 more broken eggs than in the 4 cartons the worker checked. This implies an average of 2 broken eggs per carton, which is consistent with the prediction of 2x broken eggs in the remaining cartons. Therefore, option C is the best answer.