When 2/5 of a number is subtracted from the number itself, it becomes equal to the sum of...
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When 2/5 of a number is subtracted from the number itself, it becomes equal to the sum of all the angles in a triangle ($180^\circ$). What is the number?
Show answer & explanation
Answer: A. 300
Set up the equation: x - (2/5)x = 180. Simplifying: (3/5)x = 180, so x = 180 × (5/3) = 300. The correct option is A.
Step-by-step Derivation:
Let the number be x.
According to the problem:
x - (2/5)x = 180
Combine like terms:
x(1 - 2/5) = 180
x(5/5 - 2/5) = 180
x(3/5) = 180
Solve for x:
x = 180 ÷ (3/5)
x = 180 × (5/3)
x = (180 × 5) / 3
x = 900 / 3
x = 300
Verification:
300 - (2/5 × 300) = 300 - 120 = 180 ✓