Question

Ms. Hernandez has 17 tomato plants that she wants to plant in rows. She will put 2 plants in some rows and 1 plant in the others. How many different ways can she plant the tomato plants?

Answer 1

The correct answer is:

8 ways.

Step-by-step explanation:

She will have at least one row with 2 plants, so using 17 rows with 1 plant each will not work.

She can have 15 rows with 1 plant each and 1 row with 2 plants.
She can have 13 rows with 1 plant each and 2 rows with 2 plants.
She can have 11 rows with 1 plant each and 3 rows with 2 plants.
She can have 9 rows with 1 plant each and 4 rows with 2 plants.
She can have 7 rows with 1 plant each and 5 rows with 2 plants.
She can have 5 rows with 1 plant each and 6 rows with 2 plants.
She can have 3 rows with 1 plant each and 7 rows with 2 plants.
She can have 1 row with 1 plant and 8 rows with 2 plants.

This makes 8 different ways to plant these tomatoes.

Answer 2

You just neeed to figure out the number of ways you can form 17 with the numbers 2 and 1. The easiest way is to write 17 as a function of the number of rows. If there are x rows with two plants and y rows with 1 plant, this equation is valid: 17= 2x + y, from which you can solve for y, y = 17 - 2x. Now you can give different whole values to x, to find the possible solution: x = 1 => y = 17 - 2 = 15. That means 1 row with 2 plants ans 15 rows - with 1 plant; x = 2 => y = 17 - 4 = 13; x = 3 => y = 17 - 6 = 11; x= 4 => y = 17 - 8 = 9; x = 5 => y = 17 - 10 = 7; x = 6 => y = 17 - 12 = 5; x = 7 => y = 17 - 14 = 3; x = 8 => y = 17 - 16 = 1. You cannot use x = 9, because that gives 2x = 18 and there are only 17 plants. So you have 8 different ways to plant the tomato plants using only 2 plants sin som rows and 1 plant in others (x from 1 to 8).