When 35 is subtracted from a number it becomes 80% of itself. What is 4/5 of that original number?

Introduction / Context:This is a linear equation framed via a percentage condition. The phrase “it reduced to 80%” means the new value equals 0.8 times the original number. Solve for the original, then compute 4/5 of it.

Given Data / Assumptions:

• N − 35 = 0.8N.
• Need 4/5 of N.

Concept / Approach:Rearrange the equation to isolate N. After finding N, multiply by 4/5 (or 0.8) to obtain the requested fraction of the original.

Step-by-Step Solution:N − 35 = 0.8N ⇒ N − 0.8N = 350.2N = 35 ⇒ N = 35 / 0.2 = 1754/5 of N = 0.8 * 175 = 140

Verification / Alternative check:Check the condition: 175 − 35 = 140; 80% of 175 is also 140. Consistent.

Why Other Options Are Wrong:70, 90, 120, 160 correspond to applying 4/5 to the wrong number or mis-solving the equation for N.

Common Pitfalls:Treating 80% as subtracting 80 (absolute) rather than 0.8N (relative). Always use proportional change for percentages.

Final Answer:140