This graph shows the inequality 25x+15y≥200

Question

and represents Lina's earnings for lawn mowing and dog walking, where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?

(1 point)
Responses

(20, 11.5)
(20, 11.5)

(2, 3)
(2, 3)

None of the points are a viable solution.
None of the points are a viable solution.

(10, 10)

Answer 1

To determine which point is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can substitute each point into the inequality and check if it satisfies the condition.

1. Checking the point (20, 11.5): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] Since \( 672.5 \geq 200 \), this point is a viable solution.

2. Checking the point (2, 3): \[ 25(2) + 15(3) = 50 + 45 = 95 \] Since \( 95 < 200 \), this point is not a viable solution.

3. Checking the point (10, 10): \[ 25(10) + 15(10) = 250 + 150 = 400 \] Since \( 400 \geq 200 \), this point is also a viable solution.

Based on these calculations, both (20, 11.5) and (10, 10) are viable solutions, while (2, 3) is not. If we must select just one viable point from the listed options, we can state that:

• (20, 11.5) is a viable solution.

If asked for all viable solutions:

• The options given do not allow for "multiple choices", but strictly speaking we'd mention both viable points as appropriate answers.

So, you can say (20, 11.5) is a viable solution if you need a single response.