carrie has 340 marbles to put in vases. the vases hold either 100 or 10 marbles each. which is away she can arrange the marbles
To determine the different ways Carrie can arrange the marbles in the vases, we can use a combination of mathematical reasoning and logic.
First, let's find the maximum number of vases that can be used to hold 100 marbles each. If each vase holds 100 marbles, the maximum number of such vases Carrie can fill is found by dividing the total number of marbles (340) by the number of marbles a single vase can hold (100).
340 marbles / 100 marbles per vase = 3 remainder 40
So, Carrie can use 3 vases that hold 100 marbles each, and she will have 40 marbles remaining.
Now, let's find the number of vases that can be used to hold 10 marbles each. Since the remaining marbles is 40, we can divide it by the number of marbles a single vase can hold (10).
40 marbles / 10 marbles per vase = 4
Carrie can use 4 vases that hold 10 marbles each.
Therefore, the possible ways she can arrange the marbles are as follows:
1. Use 3 vases that hold 100 marbles each and 4 vases that hold 10 marbles each.
2. Use 2 vases that hold 100 marbles each and 14 vases that hold 10 marbles each.
3. Use 1 vase that holds 100 marbles and 24 vases that hold 10 marbles each.
4. Use no vases that hold 100 marbles and 34 vases that hold 10 marbles each.
These are the four different ways Carrie can arrange her 340 marbles into vases holding either 100 or 10 marbles each.