Solve for an unknown percent in a mixed expression: Find ? such that ?% of 250 + 25% of 68 = 67.

Difficulty: Easy

Correct Answer: 20

Explanation:


Introduction / Context:
We have a linear equation in an unknown percentage. Break the expression into two parts: the unknown portion applied to one number, and a fixed percentage applied to another number. Then solve algebraically for the unknown percentage.


Given Data / Assumptions:

  • ?% of 250 + 25% of 68 = 67.
  • Let p be the unknown percent value (not decimal).


Concept / Approach:
Compute the known part first: 25% of 68. Then subtract it from 67 to isolate p% of 250. Finally, convert the resulting percent-of relation into a direct percent p by scaling.


Step-by-Step Solution:

25% of 68 = 0.25 * 68 = 17 So, p% of 250 = 67 − 17 = 50 (p/100) * 250 = 50 ⇒ p = 50 * 100 / 250 = 20


Verification / Alternative check:
Check: 20% of 250 = 50; 25% of 68 = 17; total = 67. Verified.


Why Other Options Are Wrong:
10, 12, 15, 25 yield totals other than 67 when substituted, so they do not satisfy the equation.


Common Pitfalls:
Confusing percent with decimal or failing to compute 25% of 68 accurately. Always isolate the unknown term methodically.


Final Answer:
20

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