In a quantitative aptitude style problem, 88 percent of 370 plus 24 percent of 210 minus x equals 118; what is the value of x that satisfies this equation?

Introduction / Context:
This question is a basic arithmetic and percentage calculation problem that often appears in quantitative aptitude tests. It combines percentages of given numbers into a linear equation in terms of x and asks you to solve for the unknown value. Such questions test both your comfort with percentage conversions and your ability to manipulate simple algebraic expressions.

Given Data / Assumptions:

- The expression is 88 percent of 370 plus 24 percent of 210 minus x.- The entire expression is equal to 118.- We assume all numbers are real and x is a single numeric value.

Concept / Approach:
The approach is to convert percentages into decimal form or fraction form and then perform standard arithmetic. Specifically, 88 percent is 88 divided by 100 and 24 percent is 24 divided by 100. After computing these portions of 370 and 210, combine them, subtract x, and set the result equal to 118. Finally, rearrange the equation to isolate x on one side. This method uses basic algebra and percentage calculation techniques.

Step-by-Step Solution:
Step 1: Express 88 percent of 370 as 88 divided by 100 multiplied by 370.Step 2: Compute 88 * 370 = 32560, then divide by 100 to get 325.6.Step 3: Express 24 percent of 210 as 24 divided by 100 multiplied by 210.Step 4: Compute 24 * 210 = 5040, then divide by 100 to get 50.4.Step 5: Add these two results: 325.6 plus 50.4 equals 376.Step 6: Form the equation 376 minus x equals 118, because 88 percent of 370 plus 24 percent of 210 minus x is given as 118.Step 7: Rearrange to solve for x: subtract 118 from 376 to obtain x equals 376 minus 118 equals 258.

Verification / Alternative check:
To verify, substitute x equals 258 back into the original expression. Compute 88 percent of 370 as 325.6 and 24 percent of 210 as 50.4. Their sum is 376. Then calculate 376 minus 258, which is 118. This matches the right hand side of the original equation, so x equals 258 is confirmed as the correct solution. Any other value would lead to a different result and would not satisfy the equation.

Why Other Options Are Wrong:
If x were 228, then 376 minus 228 would equal 148, not 118. If x were 248, then 376 minus 248 would equal 128. If x were 268, the result would be 376 minus 268 equals 108. If x were 278, the result would be 98. None of these match the required value of 118, so those options are incorrect.

Common Pitfalls:
Common mistakes include miscalculating the percentages, such as forgetting to divide by 100, or making arithmetic errors when adding or subtracting. Another pitfall is rearranging the equation incorrectly, for example writing x equals 118 minus 376 instead of 376 minus 118. Carefully performing each step and verifying the answer by substitution helps avoid these errors.

Final Answer:
The value of x that satisfies the equation is 258.