Question

Farmer Jan is a vegetable farmer who divides his field between broccoli crops and spinach crops. Last year, he grew 6 tons of broccoli per acre and 9 tons of spinach per acre, for a total of 93 tons of vegetables. This year, he grew 2 tons of broccoli per acre and 3 tons of spinach per acre, for a total of 31 tons of vegetables. how many acres of broccoli crops and how many acres if spinach crops does farmer jan have?​

Answer 1

There is no unique solution to this problem.

There are infinitely many solutions to this problem.

Explanation:

Let B denotes broccoli crop

Let S denotes spinach crop

Last year, he grew 6 tons of broccoli per acre and 9 tons of spinach per acre, for a total of 93 tons of vegetables.

Mathematically,

6B + 9S = 93 eq. 1

This year, he grew 2 tons of broccoli per acre and 3 tons of spinach per acre, for a total of 31 tons of vegetables.

Mathematically,

2B + 3S = 31

2B = 31 - 3S

B = (31 - 3S)/2 eq. 2

Substitute eq. 2 into eq. 1

6B + 9S = 93

6[(31 - 3S)/2] + 9S = 93

3(31 - 3S) + 9S = 93

93 - 9S + 9S = 93

- 9S + 9S = 93 - 93

0 = 0

Therefore, there is no unique solution to this problem.

Which means that there are infinitely many solutions to this problem.