School A has 30 % more students than school B. If 120 more...

School $A$ has $30 \%$ more students than school $B$. If 120 more students join school $B$, the two schools will have the same number of students. What is the sum of the number of students in school $A$ and school $B$ initially?
(A) 600
(B) 400
(C) 800
(D) 920

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Key Concepts

Percentage Increase

This concept deals with determining a value that is a certain percentage higher than another value. It involves understanding that an increase of 30% means the new amount is 130% of the original, which can be expressed as a multiplier (1.3 times the original). This is crucial when converting word statements of relative size into mathematical expressions.

Translating Word Problems into Equations

In many algebra problems, a worded scenario must be translated into one or more equations that model the relationships described. This involves defining variables for unknown quantities and setting up equations based on percentage changes or adjustments provided in the problem. It is essential for structuring the problem in a solvable format.

Solving Linear Equations

Once the scenario is modeled with an equation, solving linear equations involves isolating the variable to find its value. This typically includes combining like terms, using inverse operations, and sometimes applying substitution methods if multiple variables are involved. Mastery of this skill is key to arriving at the correct numerical solution in many algebra problems.

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