Compute the value of 40% of 265 plus 35% of 180, and find the number whose 50% equals this sum.

Introduction / Context:
This question involves a combination of percentage calculations and an equation. We are asked to find 40% of one quantity and 35% of another, add them, and then determine the number whose 50% (half) is equal to this combined value. Such problems test the ability to perform sequential percentage calculations and to set up and solve a simple linear equation in one variable.

Given Data / Assumptions:

We need to compute 40% of 265.

We also need to compute 35% of 180.

The sum of these two results equals 50% of an unknown number X.

We must find the value of this unknown number X.

Concept / Approach:
The approach is to handle the problem in two phases. First calculate the numeric value of each percentage using the formula value = (percentage / 100) * base. Then add the two values together. Second, interpret the equation 0.5 * X = sum and solve for X by dividing the sum by 0.5. This is equivalent to multiplying the sum by 2. Careful arithmetic is important to avoid simple calculation mistakes.

Step-by-Step Solution:
Step 1: Find 40% of 265.40% of 265 = (40 / 100) * 265 = 0.4 * 265.0.4 * 265 = 106.Step 2: Find 35% of 180.35% of 180 = (35 / 100) * 180 = 0.35 * 180.0.35 * 180 = 63.Step 3: Add both results.Sum = 106 + 63 = 169.Step 4: Let the required number be X, such that 50% of X equals 169.50% of X = (50 / 100) * X = 0.5 * X.So, 0.5 * X = 169.Therefore, X = 169 / 0.5 = 338.

Verification / Alternative check:
We can check by working backward. Take X = 338. Then 50% of 338 is (50 / 100) * 338 = 0.5 * 338 = 169. We already calculated that 40% of 265 plus 35% of 180 equals 169. Since both sides match, X = 338 is confirmed to be correct. This double check reduces the chance of having carried an arithmetic error unnoticed.

Why Other Options Are Wrong:

383, 253.5 and 300 are all inconsistent with the equation 0.5 * X = 169, because half of these numbers is not 169.

84.5 is actually half of 169 and represents 25% of 338, not 338 itself.

Any value other than 338 fails to satisfy the relationship that 50% of X must equal the computed sum of 169.

Common Pitfalls:
Some learners mistakenly add the percentages before applying them, or they may take 40% and 35% of the same number. Others compute the sum correctly but incorrectly solve 0.5 * X = 169 by subtracting or using the wrong inverse operation. Always remember that when a coefficient multiplies a variable, solving for the variable requires dividing by that coefficient. In this case, divide by 0.5, which is the same as multiplying by 2.

Final Answer:
The number whose 50% is equal to 40% of 265 plus 35% of 180 is 338.