Question

If \( 2x = 3y = 4z = 20 \), then \( 12xyz = \dots \)

• A. 16,000
• B. 8,000
• C. 4,000
• D. 800
• E. 10

Hint:

When given multiple equal equations, isolate each variable and calculate its value to then find the desired quantity.

Answer 1

The Correct Option is C

Step 1: Solve for the variables.
We are given that \( 2x = 3y = 4z = 20 \).
- Solving for \( x \), we get \( x = \frac{20}{2} = 10 \).
- Solving for \( y \), we get \( y = \frac{20}{3} = \frac{20}{3} \).
- Solving for \( z \), we get \( z = \frac{20}{4} = 5 \).
Step 2: Calculate \( 12xyz \).
Now we calculate: \[ 12xyz = 12 \times 10 \times \frac{20}{3} \times 5 = 12 \times 10 \times \frac{100}{3} = \frac{1200}{3} = 4000. \] Final Answer: \[ \boxed{\text{The correct answer is (C) 4,000.}} \]