Question

Use the image to answer the question.

The x- and y- axes of a coordinate plane range from 0 to 30 and 0 to 20 in increments of 5 and are labeled 'Lawns' and 'Dogs,' respectively. A line connects left parenthesis 0 comma 10 right parenthesis and left parenthesis 8 comma 0 right parenthesis.
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This graph shows the inequality 25x+15y≥200
, 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)

(10,10)


None of the points are a viable solution.

(2,3)


(20,11.5)

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Answer 1

Check which points satisfy 25x + 15y ≥ 200 and make sense as counts (whole numbers).

(10,10): 25(10)+15(10)=250+150=400 ≥ 200 — works and both are whole numbers.
(2,3): 25(2)+15(3)=50+45=95 < 200 — fails.
(20,11.5): 25(20)+15(11.5)=500+172.5=672.5 ≥ 200 but 11.5 dogs is not a realistic (whole) count.

So the viable solution is (10,10).