ray makes an array that has 4 rows of 4 counters. he wants to make two more arrays using the same number of counters. he wants more than one counter in each row. what two arrays can he make?
2 x 8 or 8 x 2.
Well, Ray certainly seems to like counting, doesn't he? Let's see what options he has:
1) Option one: Ray can make an array with 2 rows and 8 counters in each row. That would give him a total of 16 counters in his array.
2) Option two: Ray can also make an array with 8 rows and 2 counters in each row. This would also give him a total of 16 counters.
So, Ray has two choices: he can either stack his counters into two rows of 8 counters each or spread them out into eight rows of two counters each. It all depends on whether he wants his counters to be more "stacked" or "spread out". The choice is his!
To solve this problem, we can start by determining the total number of counters in the initial array. Since the array has 4 rows and 4 counters in each row, the total number of counters in the initial array is 4 x 4 = 16 counters.
Next, let's take a look at the conditions given: Ray wants to make two more arrays using the same number of counters, and he wants more than one counter in each row.
To find the arrays, we can consider the factors of 16. The factors of 16 are 1, 2, 4, 8, and 16.
Since Ray wants more than one counter in each row, we can exclude the factor 1.
Now, let's list two arrays that satisfy the conditions:
1) Array with 2 rows and 8 counters in each row:
- This array has 2 x 8 = 16 counters, which satisfies the condition of using the same number of counters.
- Both rows have more than one counter, as required.
2) Array with 8 rows and 2 counters in each row:
- This array also has 2 x 8 = 16 counters, satisfying the condition of using the same number of counters.
- All rows have more than one counter, as required.
Therefore, Ray can create two more arrays: one with 2 rows and 8 counters in each row, and another with 8 rows and 2 counters in each row.
To find out what two arrays Ray can make using the same number of counters, we need to consider the criteria given: 4 rows of 4 counters in each array, with more than one counter in each row.
First, let's determine the total number of counters. Since there are 4 rows and 4 counters in each row, Ray initially has 4 * 4 = 16 counters.
Now, the task is to distribute these 16 counters into two additional arrays, following the given criteria. We need to divide the counters into more than one counter per row.
One possible way is to create two arrays with 2 rows and 8 counters in each row:
Array 1:
- Row 1: 4 counters
- Row 2: 4 counters
Array 2:
- Row 1: 4 counters
- Row 2: 4 counters
Another possible way is by creating two arrays with 3 rows and 6 counters in each row:
Array 1:
- Row 1: 4 counters
- Row 2: 4 counters
- Row 3: 4 counters
Array 2:
- Row 1: 4 counters
- Row 2: 4 counters
- Row 3: 4 counters
So, Ray can make two additional arrays using the same number of counters: one with 2 rows and 8 counters in each row, and another with 3 rows and 6 counters in each row.