When a number is increased by 24, it becomes 115% of its original value. What is the original number?

Introduction / Context:
This problem combines a fixed numerical increase with a percentage description of the new value. Such questions check a student's ability to translate percentage statements into algebraic equations and then solve for the original number. The idea is that the final value is a certain percent of the initial value, and the difference between them is given.

Given Data / Assumptions:

• Let the original number be N.
• When 24 is added to N, the result becomes 115% of N.
• We need to find N.

Concept / Approach:
If the final value is 115% of the original number, then the final value is 1.15 * N. The question states that this final value is also equal to N + 24. Therefore, we set up an equation N + 24 = 1.15N and solve for N. This is a linear equation with one variable and can be solved by simple rearrangement.

Step-by-Step Solution:
Step 1: Let the original number be N. Step 2: After increasing N by 24, we get N + 24. Step 3: According to the problem, N + 24 = 115% of N. Step 4: Write 115% of N as 1.15N. Step 5: So the equation becomes N + 24 = 1.15N. Step 6: Bring N terms on one side: 24 = 1.15N - N = 0.15N. Step 7: Therefore N = 24 / 0.15. Step 8: Compute N = 160. Step 9: So the original number is 160.

Verification / Alternative check:
We can verify by substituting N = 160 back into the condition. N + 24 = 160 + 24 = 184. Now check 115% of 160: 1.15 * 160 = 184. The values match exactly, so N = 160 is correct.

Why Other Options Are Wrong:

• 250: 250 + 24 = 274, but 115% of 250 is 287.5, which does not match.
• 100: 100 + 24 = 124, but 115% of 100 is 115.
• 200: 200 + 24 = 224, while 115% of 200 is 230.
• 180: 180 + 24 = 204, but 115% of 180 is 207.

Common Pitfalls:
One common error is misinterpreting 115% as 1.15 plus N instead of 1.15 times N. Another frequent mistake is solving the equation incorrectly by subtracting the wrong terms or dividing by 15 instead of 0.15. Working carefully with decimal multipliers and checking the result by substitution helps avoid these mistakes.

Final Answer:
The original number is 160.