Sixty percent of two sevenths of three fourths of a certain number is 2664. What is the value of that number?

Introduction / Context:
This problem combines percentages and fractions applied successively to an unknown number. It tests your ability to convert verbal descriptions into a single algebraic expression and then solve for the original number.

Given Data / Assumptions:

• Let the unknown number be N.• We consider three fourths of N.• Then we take two sevenths of that result.• Then we take 60% of this value.• The final quantity obtained is 2664.

Concept / Approach:
Each phrase such as three fourths or sixty percent can be written as a fraction or decimal. We multiply these factors step by step to get one overall factor times N. Setting this product equal to 2664 allows us to solve for N by division.

Step-by-Step Solution:
Step 1: Three fourths of N = (3/4) * N.Step 2: Two sevenths of that = (2/7) * (3/4)N = (6/28)N = (3/14)N.Step 3: Sixty percent is 60/100 = 3/5.Step 4: Sixty percent of (3/14)N = (3/5) * (3/14)N = (9/70)N.Step 5: According to the question, (9/70)N = 2664.Step 6: Solve for N: N = 2664 * (70/9).Step 7: First compute 2664 / 9 = 296.Step 8: So N = 296 * 70 = 20720.

Verification / Alternative check:
Check by forward calculation. Three fourths of 20720 is 15540. Two sevenths of 15540 is 4440. Sixty percent of 4440 is 0.60 * 4440 = 2664, which matches the given value. This verifies the solution.

Why Other Options Are Wrong:
Values 21352, 25421 and 24150 do not reproduce 2664 when the same operations are applied. They result from incorrect simplification of fractions or arithmetic errors when multiplying or dividing.

Common Pitfalls:
Many students perform the steps in the wrong order or forget that 60% must be applied last to the already reduced value. Confusing 60% with 0.06 is another common mistake that would lead to a result ten times smaller.

Final Answer:
The required number is 20,720.