Some children are being divided into groups. The number of children is between 15&45. If the teacher puts them into groups of 5, 1 child will be left out. If he puts them in groups of 4, 1 child will be left out. At most how many children are there?
The problem can be represented by the equations:
x = 5a + 1
x = 4b + 1
where x is the total number of children, a is the number of groups when divided by 5, and b is the number of groups when divided by 4.
We need to find the maximum value of x such that both equations are satisfied.
Let's consider the possible values for a and b:
1. When a = 1, b = 4
x = 5 + 1 = 6
x = 4*4 + 1 = 17
In this case, x = 6 is not divisible by 4. Therefore, this combination is not valid.
2. When a = 2, b = 9
x = 10
x = 4*9 + 1 = 37
Both equations are satisfied for x = 10.
Therefore, the maximum number of children is 10.