There are between 50 and 60 number of eggs in a basket when loza counts by 3's, there are 2 eggs left over .when she counts by 5's, there are 4 left over.How many eggs are there in the basket?
5n+4: 54,59
3n+2: 53, ... fill in these, and you will see a match
56
To solve this problem, we can use a method called "guess and check." We start by guessing a number of eggs that could be in the basket, and then we check if it satisfies the given conditions.
Let's start with the first condition: when Loza counts by 3's, there are 2 eggs left over. This means the number of eggs in the basket must be 2 more than a multiple of 3.
Let's try guessing a number that is 2 more than a multiple of 3, such as 5. But when we count by 3's starting from 5, we get 5, 8, 11, 14, and so on. None of these numbers are between 50 and 60.
Let's try the next number, 8. Counting by 3's starting from 8, we get 8, 11, 14, 17, 20, 23, 26, and so on. This time, when we reach 26, it falls within the range of 50 to 60. So, if there are 26 eggs in the basket, the first condition is satisfied.
Now let's check the second condition: when Loza counts by 5's, there are 4 eggs left over. This means the number of eggs in the basket must be 4 more than a multiple of 5.
Starting from 26, let's count by 5's: 26, 31, 36, 41, and so on. None of these numbers satisfy the second condition.
Let's try the next number, 31. Counting by 5's starting from 31, we get 31, 36, 41, 46, 51, and so on. When we reach 51, it satisfies both conditions. So, if there are 51 eggs in the basket, both conditions are satisfied.
Therefore, there are 51 eggs in the basket.