Evaluate algebraic word problems:

A utility has three nuclear facilities which supply a total of 600 megawatts (Mw) of electricity to a particular area.  The largest facility has a total electrical result three times that of the smallest facility.  The third facility has a result that is 50 Mw more than half that of the largest facility so what is the electrical output of each of the three facilities?

Solution:

Step 1. Let x = Electrical Output of the Smallest Facility.

Step 2.             Then,

3x = Electrical Output of the Largest Facility, &

3x/2 + 50 = Electrical Output of the Third Facility.

Step 3. Total Electrical Output = Sum of the Electrical Outputs of the Three Facilities.

600 = x + 3x + 3x/2 + 50

Step 4. Solving for x:

X + 3x + 3x/2 + 50 = 600

2x/ 2 + 6x/2 + 3x/2 = 600 -50

11x/2 = 550

11x = 1100

X = 100

Solving for the other unknowns:

3x = 3(100)

3x = 300

1/2 (3x) + 50 = 150 + 50

1/2 (3x) + 50 = 150 +50

1/2 (3x) + 50 = 200

Answers:       

Electrical Output of the Smallest Facility = 100 Mw

Electrical Output of the Largest Facility = 300 Mw

Electrical Output of the Third Facility = 200 Mw

Step 5. The largest facility has a total electrical output three times in which of the smallest facility.

3(100) = 300

The other facility has an output which is 50 Mw more than half that of the largest facility.

1/2(300) + 50 = 180 + 50 = 200

The total result of the three facilities is 600 Mw.

100 + 200 + 300 = 600

Thus, the answers check.