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A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ?
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A trader with a basket of eggs finds that if he sells 3 eggs at a time...
We know that the LCM of 3 and 4 is 12. We have also been given that the maximum capacity of the egg basket is 100.
Lets list down the multiples of 12 till the number reaches 100.
12, 24, 36, 48, 60, 72, 84, 96
To leave a remained with 3 as well as 4, these numbers list above need to be one more; so we get the new numbers as follows:
13, 25, 37, 49, 61, 73, 85, 97.
The given statement also states that when 7 eggs are selected, no eggs remain. That mean we are looking for a number that is divisible by 7.
From 13, 25, 37, 49, 61, 73, 85, 97, we see that only 49 matches all the three criteria.
Hence the total number of eggs in the basket is 49
Lets list down the multiples of 12 till the number reaches 100.
12, 24, 36, 48, 60, 72, 84, 96
To leave a remained with 3 as well as 4, these numbers list above need to be one more; so we get the new numbers as follows:
13, 25, 37, 49, 61, 73, 85, 97.
The given statement also states that when 7 eggs are selected, no eggs remain. That mean we are looking for a number that is divisible by 7.
From 13, 25, 37, 49, 61, 73, 85, 97, we see that only 49 matches all the three criteria.
Hence the total number of eggs in the basket is 49
Community Answer
A trader with a basket of eggs finds that if he sells 3 eggs at a time...
Problem
A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket?
Solution
Let's assume that there are x eggs in the basket.
From the given information, we can write the following equations:
We can simplify the first two equations to:
where a and b are integers.
Substituting x from the first equation into the second equation, we get:
3a + 1 = 4b + 1
3a = 4b
This means that a is a multiple of 4 and b is a multiple of 3.
Let's assume that a = 4c. Then b = 3d, where c and d are integers.
Substituting these values into the equations for x, we get:
x = 3(4c) + 1 = 12c + 1
x = 4(3d) + 1 = 12d + 1
Since x is also a multiple of 7, we can write:
x = 7e
Now, we can substitute 7e for x in the first two equations and simplify:
Solving these equations gives us e = 1, so x = 7.
However, this solution does not satisfy the last condition that x ≤ 100.
We can find the next solution by adding 84 (the LCM of 3, 4, and 7) to 7, and we get x = 91.
We can keep adding 84 until we get a solution that satisfies x ≤ 100.
The solutions are 7, 91, and 175.
Therefore, the basket can have 7, 91, or 175 eggs in it.
A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket?
Solution
Let's assume that there are x eggs in the basket.
From the given information, we can write the following equations:
- x ≡ 1 (mod 3)
- x ≡ 1 (mod 4)
- x ≡ 0 (mod 7)
- x ≤ 100
We can simplify the first two equations to:
- x = 3a + 1
- x = 4b + 1
where a and b are integers.
Substituting x from the first equation into the second equation, we get:
3a + 1 = 4b + 1
3a = 4b
This means that a is a multiple of 4 and b is a multiple of 3.
Let's assume that a = 4c. Then b = 3d, where c and d are integers.
Substituting these values into the equations for x, we get:
x = 3(4c) + 1 = 12c + 1
x = 4(3d) + 1 = 12d + 1
Since x is also a multiple of 7, we can write:
x = 7e
Now, we can substitute 7e for x in the first two equations and simplify:
- 7e ≡ 1 (mod 3)
- 7e ≡ 1 (mod 4)
Solving these equations gives us e = 1, so x = 7.
However, this solution does not satisfy the last condition that x ≤ 100.
We can find the next solution by adding 84 (the LCM of 3, 4, and 7) to 7, and we get x = 91.
We can keep adding 84 until we get a solution that satisfies x ≤ 100.
The solutions are 7, 91, and 175.
Therefore, the basket can have 7, 91, or 175 eggs in it.
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A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ?
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A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ?.
A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ?.
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A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ?, a detailed solution for A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ? has been provided alongside types of A trader with a basket of eggs finds that if he sells 3 eggs at a time, there is only 1 egg left. If he sells 4 eggs at a time, again 1 egg is left. However if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how eggs are in the basket? Explain with reasoning ? ? theory, EduRev gives you an
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