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?
Make a table to solve.
Answer (3)
If we go for the ratio of (2 in row : 1 in row)
8:1 7:3 6:5 5:7 4:9 3:11 2:13 1:15 0:17
Therefore there are 9 possibilities
Ms. Hernandez can plant her 17 tomato plants in 9 different ways, depending on the arrangement of rows with 2 plants and rows with 1 plant. We listed all possible combinations where the total number of plants always sums to 17. Thus, by varying the number of rows with 2 plants, there are exactly 9 different configurations.
How Many Different Ways Can Ms. Hernandez Plant Her Tomato Plants?
Ms. Hernandez has 17 tomato plants, and she plans to plant them in rows, with some rows containing 2 plants and others containing 1 plant. The goal is to determine how many different ways she can plant the tomato plants.
Let's set up a table to visualize the different combinations:
Rows with 2 Plants Rows with 1 Plant
0 17
1 15
2 13
3 11
4 9
5 7
6 5
7 3
8 1
To count the total number of different ways, we can see the pattern systematically by summing the number of rows with 2 plants and ensuring the total number of plants adds up to 17:
0 rows with 2 plants, 17 rows with 1 plant
1 row with 2 plants, 15 rows with 1 plant
2 rows with 2 plants, 13 rows with 1 plant
3 rows with 2 plants, 11 rows with 1 plant
4 rows with 2 plants, 9 rows with 1 plant
5 rows with 2 plants, 7 rows with 1 plant
6 rows with 2 plants, 5 rows with 1 plant
7 rows with 2 plants, 3 rows with 1 plant
8 rows with 2 plants, 1 row with 1 plant
Therefore, there are 9 different ways Ms. Hernandez can plant her 17 tomato plants.
Ms. Hernandez can plant her 17 tomato plants in 9 different ways by varying the number of rows with 2 plants and 1 plant. The combinations are outlined in a table, showing how each arrangement sums up to 17. The total number of valid combinations is 9.
;
