35 marbles are to be put into 5 boxes. The number of marbles in each box must
be different and it must be an odd number. How many marbles are there in each
box?
so 5 odd numbers add to 35. If they are consecutive, with the smallest being x, then
5x+(2+4+6+8) = 5x+20 = 35
x = 3
So the numbers are 3,5,7,9,11
To solve this problem, we can start by dividing the total number of marbles (35) by the number of boxes (5). However, since the number of marbles in each box must be different and odd, we need to adjust our approach.
Since the problem specifies that the number of marbles in each box must be different, we can use odd numbers ranging from 1 to 9, as there are 5 boxes in total. Let's try the odd numbers starting from 1 and see if we can distribute the marbles evenly:
1 + 3 + 5 + 7 + 9 = 25
With these odd numbers, we have distributed 25 marbles, which is not equal to the total number of marbles (35). To distribute the remaining 10 marbles, we need to adjust the numbers in each box.
Since the number of marbles in each box must be odd and different from one another, we can use the following distribution:
Box 1: 1 marble
Box 2: 3 marbles
Box 3: 5 marbles
Box 4: 7 marbles
Box 5: 19 marbles
Now let's add up the marbles in each box:
1 + 3 + 5 + 7 + 19 = 35
We have successfully distributed all 35 marbles, with each box containing a different odd number of marbles. Therefore, the number of marbles in each box is as follows:
Box 1: 1 marble
Box 2: 3 marbles
Box 3: 5 marbles
Box 4: 7 marbles
Box 5: 19 marbles