Susan makes $5 per hour babysitting and $7 per hour as a lifeguard. Her goal is to make at least $140. Let x = the number of hours that Susan babysits. Let y = the number of hours that Susan works as a lifeguard. Which of the following represents three possible solutions to the problem? (1 point) Responses Image with alt text: 5 x plus 7 y greater-than-or-equal-to 140 Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y intercept of 20 and an ax intercept of 28. Shading is above the boundary line. (7,15), (14, 10), and (0,20) are three possible solutions. Image with alt text: 5 x plus 7 y less-than-or-equal-to 140 Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y intercept of 20 and an ax intercept of 28. Shading is below the boundary line. (1,15), (2,10), and (3,5) are three possible solutions. Image with alt text: 5 x plus 7 y greater-than-or-equal-to 140 Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y intercept of 28 and an x intercept of 20. Shading is above the boundary line. (5,15), (10,20), and (15,30) are three possible solutions.

Question

Susan makes $5 per hour babysitting and $7 per hour as a lifeguard. Her goal is to make at least $140. Let x = the number of hours that Susan babysits. Let y = the number of hours that Susan works as a lifeguard. Which of the following represents three possible solutions to the problem? (1 point) Responses Image with alt text: 5 x plus 7 y greater-than-or-equal-to 140 Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y intercept of 20 and an ax intercept of 28. Shading is above the boundary line. (7,15), (14, 10), and (0,20) are three possible solutions. Image with alt text: 5 x plus 7 y less-than-or-equal-to 140 Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y intercept of 20 and an ax intercept of 28. Shading is below the boundary line. (1,15), (2,10), and (3,5) are three possible solutions. Image with alt text: 5 x plus 7 y greater-than-or-equal-to 140 Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y intercept of 28 and an x intercept of 20. Shading is above the boundary line. (5,15), (10,20), and (15,30) are three possible solutions.

Answer 1

The correct representation of three possible solutions to the problem is:

\[5x + 7y \geq 140\]

Answer 2

The correct answer is:

Image with alt text: 5x + 7y ≥ 140

Image with alt text: The first quadrant of a coordinate plane is shown with the x axis labeled Babysitting and the y axis labeled Lifeguard. A solid boundary line is graphed with a y-intercept of 20 and an x-intercept of 28. Shading is above the boundary line. (7,15), (14, 10), and (0,20) are three possible solutions.

Answer 3

The problem states that Susan makes $5 per hour babysitting and $7 per hour as a lifeguard, and her goal is to make at least $140.

To represent the number of hours Susan babysits, let's use the variable x. Similarly, let's use the variable y to represent the number of hours she works as a lifeguard.

Given this information, we can set up an equation to represent Susan's earnings:

5x + 7y ≥ 140

This equation states that the total earnings from babysitting (5x) plus the total earnings from lifeguarding (7y) should be greater than or equal to $140.

Now, let's examine the given options:

Option 1: 5x + 7y ≥ 140 (Textual representation without graphical visualization)
This option aligns with our equation, so it is a possible solution to the problem.

Option 2: The first quadrant of a coordinate plane is shown with the x-axis labeled Babysitting and the y-axis labeled Lifeguard. A solid boundary line is graphed with a y-intercept of 20 and an x-intercept of 28. Shading is above the boundary line. (7,15), (14, 10), and (0,20) are three possible solutions.
This option provides a graphical representation of the problem. The solid boundary line with a y-intercept of 20 and an x-intercept of 28 represents the equation 5x + 7y = 140. As the shading is above the boundary line, any points on or above it will satisfy the inequality 5x + 7y ≥ 140. The given points (7,15), (14,10), and (0,20) lie on or above the boundary line and hence satisfy the inequality. Therefore, this option is also a possible solution.

Option 3: 5x + 7y ≤ 140 (Textual representation without graphical visualization)
This option represents the inequality in the opposite direction. The problem statement mentions that Susan's goal is to make at least $140, so the earnings should be greater than or equal to $140, not less than or equal to. Hence, this option is not a valid solution.

Option 4: The first quadrant of a coordinate plane is shown with the x-axis labeled Babysitting and the y-axis labeled Lifeguard. A solid boundary line is graphed with a y-intercept of 28 and an x-intercept of 20. Shading is above the boundary line. (5,15), (10,20), and (15,30) are three possible solutions.
This option provides another graphical representation, but the solid boundary line with a y-intercept of 28 and an x-intercept of 20 represents a different equation. The correct equation should have a y-intercept of 140/7 and an x-intercept of 140/5, which is not depicted in this graph. Therefore, this option is not a valid solution either.

In conclusion, the correct answer is Option 1: 5x + 7y ≥ 140 or Option 2: The first quadrant of a coordinate plane is shown with the x-axis labeled Babysitting and the y-axis labeled Lifeguard. A solid boundary line is graphed with a y-intercept of 20 and an x-intercept of 28. Shading is above the boundary line. (7,15), (14, 10), and (0,20) are three possible solutions.