Answer:
31.2 g
Explanation:
You want to know the average weight of the remaining eggs if two from a dozen with average weight 32 g are broken, and their weights are 35 and 37 g.
Relative to average
The two broken eggs differ from average by ...
(35 -32) +(37 -32) = 3 +5 = 8 . . . . . grams
The remaining eggs must differ from that average by the opposite amount, a total of -8 g.
Distributed over 10 eggs, this difference is -0.8 g, so the average weight of the remaining eggs is 32 -0.8 = 31.2 g.
The average weight of the remaining 10 is 31.2 g.
New sum
The average weight is the sum of all weights divided by the number of eggs:
avg = W/N
W = N·avg = 12·32 g = 384 g
The new sum of weight will be this amount less the weights of the broken eggs:
W' = 384 g -35 g -37 g = 312 g
The new number of eggs is 2 fewer: N' = 12 -2 = 10.
So, the new average weight is ...
avg' = W'/N' = 312 g/10 = 31.2 g
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Additional comment
By working with the differences from average, we don't have to figure the old and new sums. We're only concerned with the way that sum changes, and the average amount of that change. Often, this means we can solve the problem using only mental arithmetic.
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