You want to earn at least $150 doing both sets of jobs. You earn $15.00 an hour to mow lawns and $10.00 to wash cars.

Answer 1

Let x be the number of the hours to mow lawns, and y be the number of the cars to wash cars.

Earn per hour to mow lawns job 15 dollars and earn per car to wash cars job 10 dollars.

Write an algebraic expression for the current situation.

Number of hours for lawn job * Hourly rate + Number of cars for washing * Rate for washing each car ≥ Total amount earned by doing both jobs.

(Note: Need to earn at least 150$, so greater than or equal to symbol used)

 

So, the inequality is 15x + 10y ≥ 150.

 

The graph of the equality 15x+10y=150 is the boundary of the region. Since the inequality ≥, the boundary is drawn as a solid line.

 

To graph the boundary line, find the x - intercept and y - intercept of the line.

To find the y - intercept, substitute the value of x = 0 in the original equation.

The y - intercept is 15, so the graph intersects the y - axis at(0, 15).

 

To find the x - intercept, substitute the value of y = 0 in the original equation.

The x - intercept is 10, so the graph intersects the x - axis at (10, 0).

 

To draw inequality 15x+10y≥150 follow the steps.

1.  Draw a coordinate plane.

2.  Plot the points and draw a line through these points.

3.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute the value of (x, y) = (0, 0) in the original inequality.

15(0)+10(0)≥150 ⇒ 0≥150.

4.  Since the above statement is false, shade the region that does not contain point (0, 0).

 

More than 150$ can be earned by selecting any (x, y) values within the shaded region and on the line.