Question

Edward has four boxes of marbles. He notices that the product of the number of marbles in box 2,3 and 4 is identical to the number of marbles in box 1. When he adds up the number of marbles in box 2,3 and 4, they add up to 36. The difference in the number of marbles in box 2 and 4 is 1. Find the number of marbles in each of the boxes.

Answer 1

Let's say box 2 has x marbles.
Since the difference in the number of marbles in box 2 and 4 is 1, that means box 4 has x-1 marbles.
Then, the number of marbles in box 3 can be represented as (36 - x - (x-1)).
Simplifying, we get (36 - 2x + 1) = 37 - 2x.
Since the product of the number of marbles in box 2,3 and 4 is identical to the number of marbles in box 1, that means box 1 has (x * (37 - 2x)).
Therefore, we have x * (37 - 2x) = 37 * (x-1) + (x-1).
Expanding the right side of the equation, we get x * (37 - 2x) = 37x - 37 + x - 1.
Combining like terms, we get x^2 - 36x + 36 = 0.
Factoring the equation, we get (x - 6)(x - 6) = 0.
Therefore, x = 6.
So, box 2 has 6 marbles, box 4 has 6-1 = 5 marbles, and box 3 has (36 - 6 - 5) = 25 marbles.
And, box 1 has 6 * 25 = 150 marbles.
Thus, the number of marbles in each of the boxes is as follows:
Box 1: 150 marbles
Box 2: 6 marbles
Box 3: 25 marbles
Box 4: 5 marbles. Answer: \boxed{150, 6, 25, 5}.

Answer 2

A perfect number is an integer greater than zero. When we add up all of the factors less than that number, we get that number. For example, we have the first perfect number 6. The factors of 6 less than itself is 1,2,3. 1+2+3=6. Find another perfect number

Answer 3

The next perfect number after 6 is 28.

The factors of 28 less than itself are 1, 2, 4, 7, and 14.

1 + 2 + 4 + 7 + 14 = 28.

So, 28 is another perfect number.