there are between 50 and 60 eggs in a basket. when abebe counts by 3's,there are 2 eggs left over. when he counts by 5's, there are 4 left over.
how many eggs are there in the basket?
The fact that he counts by 3’s and has 2 left over tells me that the remainder is 2 when dividing the answer by 3.
Same goes for 4 left over when counting by 5’s.
so the possibilities are 54 and 59
Now divide those by 3 to see which works.
To solve this problem, we can use a common analytical technique called "system of equations" by setting up two equations based on the given information.
Let's define the number of eggs in the basket as "E." We know that when Abebe counts by 3's, there are 2 eggs left over. This means that E is two more than a multiple of 3. So, we can represent this information with the equation:
E ≡ 2 (mod 3) ----- Equation 1
Similarly, when Abebe counts by 5's, there are 4 eggs left over. This implies that E is four more than a multiple of 5. So, we can represent this information with the equation:
E ≡ 4 (mod 5) ----- Equation 2
Now, to solve the system of equations, we need to find a value of E that satisfies both Equation 1 and Equation 2.
We can start by listing down the values for E that satisfy each equation:
When E ≡ 2 (mod 3):
E = 2, 5, 8, 11, 14, 17, 20, 23, 26, ...
When E ≡ 4 (mod 5):
E = 4, 9, 14, 19, 24, 29, 34, 39, 44, ...
From the two lists, we can notice that the number 14 appears in both. Therefore, the number of eggs in the basket must be 14.
So, there are 14 eggs in the basket.