Scale one percentage to another: If 37 1/2% of a number is 900, then find 62 1/2% of the same number.

Introduction / Context:
The percentages 37 1/2% and 62 1/2% are complementary to 100% and can be expressed as simple fractions (3/8 and 5/8). This makes computing the whole and rescaling straightforward.

Given Data / Assumptions:

• 37.5% = 3/8 of the number equals 900.
• We seek 62.5% = 5/8 of the number.

Concept / Approach:
From (3/8) * N = 900, solve for N. Then compute (5/8) * N for the desired percentage.

Step-by-Step Solution:

Verification / Alternative check:
Check: 3/8 of 2400 is 900 (given) and 5/8 of 2400 is 1500. The two add to the whole 2400, confirming consistency.

Why Other Options Are Wrong:

• 1200 and 1350 are undershoots of 5/8 of 2400.
• 540 corresponds to 22.5% of 2400, not 62.5%.
• 1800 equals 75% of 2400, not 62.5%.

Common Pitfalls:
Not recognizing the handy fraction forms of 37 1/2% and 62 1/2%, which greatly simplify the arithmetic.

Final Answer:
1500