Question

1. molly has 20 tomato plants to arrange in her garden. what are all the ways molly can arrange the tomato plants in an array? chart with columns rows and plants in each row and empty boxes for input

Explanation:

Step1: Find factor pairs of 20

We need to find all pairs of positive integers \((r, p)\) such that \(r\times p = 20\), where \(r\) is the number of rows and \(p\) is the number of plants per row.
The factor pairs of 20 are:

• When \(r = 1\), \(p=\frac{20}{1}=20\)
• When \(r = 2\), \(p=\frac{20}{2}=10\)
• When \(r = 4\), \(p=\frac{20}{4}=5\)
• When \(r = 5\), \(p=\frac{20}{5}=4\)
• When \(r = 10\), \(p=\frac{20}{10}=2\)
• When \(r = 20\), \(p=\frac{20}{20}=1\)

Step2: Fill the table

Now we fill the table with these values:

Rows	plants in Each Row
2	10
4	5
5	4
10	2
20	1

Answer:

The ways to arrange are: 1 row with 20 plants, 2 rows with 10 plants each, 4 rows with 5 plants each, 5 rows with 4 plants each, 10 rows with 2 plants each, 20 rows with 1 plant each. The filled table is as above.