Luke is planting seeds in pots. Luke has eighty-four seeds. Luke wants to have the same number of seeds in each pot. Luke does not want to plant more than fourteen seeds in each pot. Luke only has twenty-five pots. What are three ways Luke can plant the same number of seeds in each pot?
To find three ways Luke can plant the same number of seeds in each pot, we need to determine the factors of the total number of seeds Luke has (84).
First, let's list down the factors of 84:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Now, let's consider the condition that Luke wants to have no more than 14 seeds in each pot. Among the factors listed, we can eliminate the numbers that are greater than 14.
After eliminating the numbers greater than 14, we are left with the following potential ways to have the same number of seeds in each pot:
1, 2, 3, 4, 6, 7, 12, 14
Now, let's consider the number of pots Luke has (25). We need to find three ways to distribute the seeds in each pot while maintaining an equal number, using the remaining factors.
1) If Luke wants to have 1 seed in each pot, he can distribute the 1 seed among all 25 pots.
2) If Luke wants to have 2 seeds in each pot, he can distribute 2 seeds among 12 pots, leaving 1 pot empty.
3) If Luke wants to have 4 seeds in each pot, he can distribute 4 seeds among 6 pots, leaving 1 pot empty.
Therefore, three ways Luke can plant the same number of seeds in each pot are:
1) 1 seed in each pot
2) 2 seeds in 12 pots, leaving 1 pot empty
3) 4 seeds in 6 pots, leaving 1 pot empty