Maths: Algebra Word Problems: Translating Real-World Relationships

Word problems often feel like a puzzle, but at their heart, they are about spotting relationships and turning them into algebra. In this case, the relationship is proportional: the total cost of apples grows steadily with the number bought. The core move is translating that real-world situation into a simple expression, where a variable like n stands for an unknown quantity—here, the number of apples—and a constant represents the fixed rate of change. Understanding the parts of your expression is just as important as writing it. The coefficient, 3, is not a random number; it is the price per single apple, the unit rate that connects n to the total cost. When you multiply 3 by n, you are scaling that unit cost across however many apples are purchased. This idea extends far beyond fruit: any situation with a constant rate—distance at a steady speed, pay per hour, ingredients per serving—follows the same structure. Once you see that the coefficient carries the “per one” meaning, you can interpret, compare, and calculate with confidence, whether you are working with 6 apples or 600.