Question

You earn $15 an hour mowing lawns and $10 an hour washing windows.

You want to make $400 in one week. An algebraic model for your earnings is 15x + 10y = 400, where x is the number of hours mowing lawns and y is the number of hours washing windows. 1)What are your earnings for 3 hours of mowing and 5 hours of 952 window washing?
2)Solve the equation for y.
3)Sketch a graph of the equation:3. 5.

Answer 1

To find the earnings for the given hours, substitute the values into the equation. To solve the equation for y, isolate y. To sketch the graph, plot points, and connect them with a line.

Step-by-step explanation:

1) To find your earnings for 3 hours of mowing and 5 hours of window washing, we can substitute the values into the algebraic model. So, we have:

15(3) + 10(5) = 45 + 50 = 95

Therefore, your earnings for 3 hours of mowing and 5 hours of window washing would be $95.

2) To solve the equation for y, we need to isolate y on one side. So, we have:

15x + 10y = 400

10y = 400 - 15x

y = (400 - 15x) / 10

Therefore, the equation solved for y is y = (400 - 15x) / 10.

3) To sketch a graph of the equation, we can start by plotting two points on the graph. We can choose any values for x and find the corresponding y values using the equation. For example, if we choose x = 0, we have:

y = (400 - 15(0)) / 10 = 40

So, one point on the graph is (0, 40). Similarly, if we choose x = 10, we have:

y = (400 - 15(10)) / 10 = 25

So, another point on the graph is (10, 25). By connecting these two points, we can draw a straight line to represent the equation.