Difficulty: Easy
Correct Answer: 200
Explanation:
Introduction / Context:
This is a classic reverse percentage problem involving an absolute increase that transforms a number into a specified percentage of itself. Such questions test how well you can translate verbal percentage descriptions into equations and then solve for the unknown original value.
Given Data / Assumptions:
Concept / Approach:
The key idea is to express “119% of the original number” in algebraic form as 1.19N. Since the increased value N + 38 equals 1.19N, we set up the equation N + 38 = 1.19N. Then, we solve this equation by moving terms involving N to one side and constants to the other. This is a simple linear equation once the percentage is converted to decimal form.
Step-by-Step Solution:
Step 1: Let the original number be N.
Step 2: After increasing by 38, the new number is N + 38.
Step 3: The new number is 119% of the original, so write N + 38 = 119% of N = 1.19N.
Step 4: Rearrange the equation: N + 38 = 1.19N implies 38 = 1.19N - N = 0.19N.
Step 5: Solve for N: N = 38 / 0.19.
Step 6: Compute N = 200.
Verification / Alternative check:
Check the answer by substituting N = 200 back into the situation. Increase 200 by 38 to get 238. Now, calculate 119% of 200: (119 / 100) * 200 = 238. The increased value exactly matches 119% of the original, confirming the solution is correct.
Why Other Options Are Wrong:
342, 456, 570, 150: If any of these were the original number, then adding 38 and checking whether the result is 119% of the assumed original quickly shows that the equality does not hold. For example, if N = 150, N + 38 = 188, but 119% of 150 is 178.5, not 188.
Common Pitfalls:
Some students mistakenly treat 119% as 0.19 instead of 1.19, or they write 119N instead of 1.19N. Others forget that the 38 is an absolute increase, not a percentage increase. Always convert percentage phrases carefully and set up the equation with correct decimal values.
Final Answer:
The original number is 200.
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