When 1/5 of a number is subtracted from the number itself, it becomes equal to the sum of...
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When 1/5 of a number is subtracted from the number itself, it becomes equal to the sum of all the angles in a triangle. What is the number?
Show answer & explanation
The sum of angles in a triangle is 180°. Setting up the equation: x - x/5 = 180, which simplifies to 4x/5 = 180. Solving for x gives x = 450. We can verify: 450 - 450/5 = 450 - 90 = 360... wait, that's incorrect. Let me recalculate: 450 - 90 = 360 ≠ 180. The correct answer is actually B (300), since 300 - 300/5 = 300 - 60 = 240 ≠ 180 either. Rechecking: x - x/5 = 180 → 4x/5 = 180 → x = 225. Verification: 225 - 45 = 180. ✓
Step-by-step Derivation:
Let the number be x.
Given condition: x - (1/5)x = 180 (sum of angles in triangle)
Step 1: Combine like terms
x - x/5 = 180
(5x - x)/5 = 180
4x/5 = 180
Step 2: Solve for x
4x = 180 × 5
4x = 900
x = 900/4
x = 225
Step 3: Verification
225 - (1/5)(225) = 225 - 45 = 180 ✓
The answer is 225.