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.