Find the value of the missing term in the equation: 56% of 870 plus 82% of 180 equals 32% of 90 plus an unknown number. What is this unknown number?

Introduction / Context:
This question presents a percentage equation where an unknown number appears on one side along with another percentage expression. The goal is to compute each percentage term, simplify both sides, and then solve for the unknown number. Such questions check accuracy with percentage calculations and algebraic manipulation in a single step.

Given Data / Assumptions:

We have 56% of 870.

We also have 82% of 180.

The sum of these two values equals 32% of 90 plus an unknown number, say X.

We need to find the value of X that satisfies this equation.

Concept / Approach:
The method is to evaluate each percentage separately using value = (percentage / 100) * base. First compute 56% of 870 and 82% of 180, and add them to get the left hand side. Then compute 32% of 90 on the right hand side. Finally, express the equation as left side = 32% of 90 + X and solve for X by subtracting the known percentage value from the left side total. Careful arithmetic is essential due to multiple percentage operations.

Step-by-Step Solution:
Let the unknown number be X.Compute 56% of 870: (56 / 100) * 870 = 0.56 * 870.0.56 * 870 = 487.2.Compute 82% of 180: (82 / 100) * 180 = 0.82 * 180.0.82 * 180 = 147.6.Left hand side total = 487.2 + 147.6 = 634.8.Compute 32% of 90: (32 / 100) * 90 = 0.32 * 90 = 28.8.According to the question, 634.8 = 28.8 + X.So X = 634.8 - 28.8 = 606.Therefore, the unknown number is 606.

Verification / Alternative check:
Substitute X = 606 back into the equation. Right hand side becomes 32% of 90 plus 606. We already have 32% of 90 = 28.8. So right hand side = 28.8 + 606 = 634.8. Left hand side was computed as 56% of 870 plus 82% of 180 = 634.8. Since both sides are equal, the equation is satisfied and X = 606 is correct.

Why Other Options Are Wrong:

777, 666, 789 and 696 all give right hand side totals that do not equal 634.8 when added to 28.8.

Only X = 606 makes the right hand side equal to the left hand side sum of 634.8.

Common Pitfalls:
Some students accidentally add 56 and 82 as percentages before applying them, or they compute 32% of 870 by mistake. Another common error is to subtract incorrectly when isolating X, for example adding 28.8 instead of subtracting it. A few learners also misplace decimal points when multiplying by percentages such as 0.56 and 0.82. Writing each step clearly and rechecking arithmetic helps avoid these mistakes.

Final Answer:
The unknown number that satisfies the given percentage equation is 606.