If 20% of (x + y) is equal to 50% of (x − y), what is x : y?

Concept

A percentage equation can be converted into an algebraic equation by replacing each percentage with its decimal or fractional value.

To find x : y, simplify the equation until it gives x/y directly, with y nonzero because the ratio is defined.

Application

1. Translate the statement: 0.2(x + y) = 0.5(x − y).

2. Multiply both sides by 10 to clear decimals: 2(x + y) = 5(x − y).

3. Expand both sides: 2x + 2y = 5x − 5y.

4. Collect like terms: 2y + 5y = 5x − 2x, so 7y = 3x.

5. Divide by 3y: x/y = 7/3.

Cross-check

Let x = 7k and y = 3k. Then 20% of (x + y) = 20% of 10k = 2k, while 50% of (x − y) = 50% of 4k = 2k, so the original equality is reproduced.

Result

Therefore, x : y = 7 : 3.