Percentage increase

Statement

The price of a cinema ticket rises by $12\%$ and reaches $7{,}28$ EUR. What was it before?

Solution

Unknown. $P=$ original price. $P\cdot 1{,}12=7{,}28 \implies P=\boxed{6{,}50}\text{ EUR}$

Generalisation. If a value after an increase of $p\%$ is $V$, the value before was $V/(1+p/100)$ — never $V\cdot(1-p/100)$ (a classic mistake, linking back to the chapter on percentages).

Connections

Topics: First-degree equations
Concepts: Equation · Percentage
Methods: Percentage problem
Skills: Modelling · Solving equations
Exercise type: Word problem