Question

A lawn care store makes a profit of $89.00 for every push mower sold and $236.00 for every riding lawn mower sold. The owner would like to make at least $621.00 a day from the sales of push and riding lawn mowers. Let x = the number of push mowers sold. Let y = the number of riding mowers sold. Which of the following is a list of 3 possible solutions to the graph?(1 point)
Responses

(3,1), (4,2), (1,1)
(3,1), (4,2), (1,1)

(1,2), (2,2), (3,1)
(1,2), (2,2), (3,1)

(3,2), (2,3), (1,4)
(3,2), (2,3), (1,4)

(2,1), (2,2), (2,3)

Answer 1

To find the possible solutions to the graph, we need to find the values of x and y that satisfy the equation:

89x + 236y ≥ 621

Let's test each option:

Option 1: (3,1), (4,2), (1,1)
Plugging in (3,1):
89(3) + 236(1) = 267 + 236 = 503 (not greater than 621)
Plugging in (4,2):
89(4) + 236(2) = 356 + 472 = 828 (greater than 621)
Plugging in (1,1):
89(1) + 236(1) = 89 + 236 = 325 (not greater than 621)

Option 2: (1,2), (2,2), (3,1)
Plugging in (1,2):
89(1) + 236(2) = 89 + 472 = 561 (not greater than 621)
Plugging in (2,2):
89(2) + 236(2) = 178 + 472 = 650 (greater than 621)
Plugging in (3,1):
89(3) + 236(1) = 267 + 236 = 503 (not greater than 621)

Option 3: (3,2), (2,3), (1,4)
Plugging in (3,2):
89(3) + 236(2) = 267 + 472 = 739 (greater than 621)
Plugging in (2,3):
89(2) + 236(3) = 178 + 708 = 886 (greater than 621)
Plugging in (1,4):
89(1) + 236(4) = 89 + 944 = 1033 (greater than 621)

Option 4: (2,1), (2,2), (2,3)
Plugging in (2,1):
89(2) + 236(1) = 178 + 236 = 414 (not greater than 621)
Plugging in (2,2):
89(2) + 236(2) = 178 + 472 = 650 (greater than 621)
Plugging in (2,3):
89(2) + 236(3) = 178 + 708 = 886 (greater than 621)

Therefore, the list of 3 possible solutions to the graph is option 3: (3,2), (2,3), (1,4)