There are between 50 and 60 number of eggs in basket when loza counts by 3 second there are 2 eggs left over when she countw by 5 second there are 4 left over how many eggs are there in the basket
3n+2: 50,53,56,59
5n+4: 54,59
So, what do you think?
59
To find the number of eggs in the basket, we can set up a system of equations based on the given information.
Let's assume the number of eggs in the basket is represented by 'x'.
According to the given information, when Loza counts by 3 seconds, there are 2 eggs left over. This can be expressed as: x ≡ 2 (mod 3)
Similarly, when Loza counts by 5 seconds, there are 4 eggs left over. This can be expressed as: x ≡ 4 (mod 5)
To solve this system of equations, we can use the Chinese Remainder Theorem (CRT). The CRT states that if we have a set of equations in the form x ≡ a (mod m) and x ≡ b (mod n), where m and n are coprime (having no common factors), then there exists a unique solution for x modulo (m * n).
In this case, 3 and 5 are coprime, so we can use CRT to find the solution.
Let's solve the system of equations step by step:
Step 1: Solve x ≡ 2 (mod 3) and x ≡ 4 (mod 5) individually.
For x ≡ 2 (mod 3), the possible solutions are 2, 5, 8, 11, 14, ...
For x ≡ 4 (mod 5), the possible solutions are 4, 9, 14, 19, 24, ...
Step 2: Find the common solution from the two sets of possible solutions.
We can see that 14 satisfies both equations, x ≡ 2 (mod 3) and x ≡ 4 (mod 5).
Therefore, the number of eggs in the basket is 14.
Hence, there are 14 eggs in the basket.