Agardener wants to try different combinations of fertilizer (none, 1 cup, 2 cups) and mulch (none, wood chips, pine needles, plastic) to determine which combination produces the highest yield for a variety of green beans. he has 60 green-bean plants to use in the experiment. if he wants an equal number of plants to be assigned to each treatment, how many plants will be assigned to each treatment?

5

Step-by-step explanation:

First lets identify the number of treatments possible.

1st possibility: no fertilizer, no mulch

2nd possibility: no fertilizer, wood chips

3rd possibility: no fertilizer, pine needles

4th possibility: no fertilizer, plastic

5th possibility: 1 cup fertilizer, no mulch

6th possibility: 1 cup fertilizer, wood chips

7th possibility: 1 cup fertilizer, pine chips

8th possibility: 1 cup fertilizer, plastic

9th possibility: 2 cup fertilizer, no mulch

10th possibility: 2 cup fertilizer, wood chips

11th possibility: 2 cup fertilizer, pine chips

12th possibility: 2 cup fertilizer, plastic

Or we can simply calculate no. of possibilities by elements in set a x elements in set b

Total no. of possibilities = 3 x 4 = 12

To find no. of plants for each treatment divide total number of plants by the total treatments possible.

No. of plants for each treatment = total number of plants/ total number of treatments possible

No. Of plants for each treatment = 60/12

No. of plants for each treatment = 5

no solution exists the way you wrote the equation.