Question

A farmer wants to plant peas and carrots on no more than 300 acres of his farm. If x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution? (−25, 100) (380, −160) (150, 145) (100, 250)

Answer 1

Answer:

The answer is C.

Step-by-step explanation:

You can't have a negative number of peas or carrots, so A and B are out. 1

00+250=350 which is more than 300.

150+145 = 295 which is less than 300.

So the answer is C.

Answer 2

The solutions of an equation are the true values of the equation.

The only viable solution is (c) (150, 145)

Let x represent peas and y represents carrots.

So, the constraints are:

$\mathbf{x , y \ge 0}$ ---- i.e. the values of x and y cannot be 0

$\mathbf{x + y \le 300}$ ---- i.e. the sum of x and y cannot exceed 300

$\mathbf{x , y \ge 0}$  means that options (a) and (b) are wrong.

This is so, because:

(-25, 100) and (380, -160) contain negative values of x or y

$\mathbf{x + y \le 300}$ means that option (d) is wrong.

This is so, because:

The sum of (100, 250) exceeds 300

Hence, the only viable solution is (c) (150, 145)

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