This section shows how to solve verbal descriptions of linear equations.

Let's say that you were given the problem below:

Lawns Beautiful charged Mrs. Garcia $119.00 for plants plus $25.00 per hour for a landscape designer to complete the landscaping of her yard. The total charge was $253.00. For about how long did the designer work to complete the landscaping of Mrs. Garcia's yard?

The first thing that you would do is to write an equation that represents the situation.

So if you let x = number of hours to complete the job, the equation that represents this situation would be: 119 + 25x = 253

You have two different methods that you could use to solve the equation.

Method 1: Solve the given equation for x algebraically.

  119 + 25x = 253
 -119           -119


        

25x 25 = 134 25
              x = 5.36

The landscape designer worked for approximately 5 hours to complete the job.

Method 2: Graph the equation using a graphing calculator.

Text: Step 1: Press Y= and enter the first half of the equation '119 + 25x' into Y1 and the second half of the equation '253' into and the second half of the equation '253' into Y2. Step 2: Press 'Window' and set appropriate parameters for this situation. Step 3: Press '2nd' 'Trace' and scroll down to'5' (intersect). Then press 'Enter'. Step 4: Move the cursor close to the intersection point on the 'first curve' (Y1) and press 'Enter'. Move the cursor close the intersection point on the 'second curve' (Y2) and press 'Enter'. The calculator should now say Guess. Press 'Enter' and the intersection point will be shown at the bottom of the calculator screen.

The x-value represents the number of hours worked. The calculator shows that it took approximately 5 hours to complete the landscaping of Mrs. Garcia's lawn.

Practice: Determine the answer to the problem below on your own paper.

The lengths of the legs of an isosceles triangle are each twice the length of its base. If the perimeter of the triangle is 30 inches, what is the length of its base?

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The length of the base is 6 inches. Close Pop Up