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.

Question

Write the equation and graph the inequality.

Answer 1

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

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 (≥) is 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.