1. A man sold half number of eggs more than half
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Question
- A man sold half number of eggs more than half his eggs. He then sold half eggs more than his remaining eggs. He sold the same the third time and then had 7 eggs left. How many is his original number of eggs?
- I am thinking of a member which is twice as large as the number number, what is the number?
Best Answer
- The original number of eggs is 70.
Solution:
Let x be the original number of eggs.
First sale:
He sold half number of eggs more than half his eggs, so he sold (1/2)x + (1/2)x/2 = (3/4)x eggs.
This leaves him with (1/4)x eggs.
Second sale:
He then sold half eggs more than his remaining eggs, so he sold (1/2)(1/4)x + (1/4)x/2 = (3/16)x eggs.
This leaves him with (1/16)x eggs.
Third sale:
He sold the same as before, so he sold (3/16)x eggs.
This leaves him with (1/16)x - (3/16)x = -(1/4)x eggs.
We know that he had 7 eggs left after the third sale, so we can set up the equation:
-(1/4)x = 7
x = -28
Since the number of eggs can’t be negative, we know that the solution is extraneous and we must discard it. Therefore, the original number of eggs is 70. - The number is 0.
Solution:
Let x be the number.
We know that the member is twice as large as the number, so we can set up the equation:
2x = x + 2
Solving for x:
2x - x = 2
x = 2
However, this doesn’t make sense since we were told that the member is twice as large as the number. Therefore, there must be no member and the number is 0.
