a box contains more than 25 but fewer than 40 balls.When the balls are counted by 3 there is 1 left over.When the balls are counted by 5 there are 2 left over.How many balls are in the box?
37
To solve this problem, we can use algebraic reasoning and perform some calculations based on the given information.
Let's assume the number of balls in the box is represented by the variable "x".
According to the problem, when the balls are counted by 3, there is 1 left over. This can be expressed as the equation: x ≡ 1 (mod 3).
Similarly, when the balls are counted by 5, there are 2 left over. This can be expressed as the equation: x ≡ 2 (mod 5).
To find the number of balls, we need to solve the system of congruences:
x ≡ 1 (mod 3)
x ≡ 2 (mod 5)
We can solve this system using the Chinese Remainder Theorem or by trial and error.
One approach is to list out the values of x that satisfy the given congruences and check each one to see if it falls within the given range of more than 25 but fewer than 40 balls:
x = 7, 17, 22, 32, 37, 47, 52, 62, 67, 77, ...
From this list, we can see that the number of balls that fits the given criteria is 32.
Therefore, there are 32 balls in the box.