Solving Algebraic Word Problems:
What are the capacities of two water storage tanks in a nuclear facility if one holds 9 gallons less than three times another, and their whole capacity is 63 gallons?
Solution:
Step 1. Let x = Capacity of the Smaller Tank
Step 2. Then, 3x - 9 = Capacity of the Larger Tank
Step 3. Total Capacity = Capacity of the Smaller Tank + Capacity of the Larger Tank
63 = x + (3x - 9)
Step 4. Solving for x:
x + (3x - 9) = 63
4x - 9 = 63
4x = 63 + 9
4x = 72
x = 18
Solving for the other unknown:
3x - 9 = 3(18) - 9
3x - 9 = 54 - 9
3x - 9 = 45
Answer:
Capacity of the Smaller Tank = 18 gallons
Capacity of the Larger Tank = 45 gallons
Step 5. The larger tank holds 9 gallons less than three times the smaller tank.
3(18) - 9 = 54 - 9 = 45
The total capacity of the two tanks is 63 gallons.
18 + 45 = 63
Therefore, the answers check.