7.2. Harry, Ron, and Hermione wanted to buy identical waterproof cloaks. However, they lacked the money: Ron was short by a third of the cloak's price, Hermione by a quarter, and Harry by one fifth of the cloak's price. When the price of the cloak dropped by 9.4 sickles during a sale, the friends pooled their savings and bought three cloaks, spending all their money. How many sickles did one cloak cost before the price reduction?
Answer: 36 sickles.

Solution. Let the initial cost of the cloak be $x$ sickles, then Ron had $\frac{2}{3} x$ sickles, Hermione had $\frac{3}{4} x$ sickles, and Harry had $\frac{4}{5} x$ sickles. During the sale, the cloak cost $(x-9.4)$ sickles, and three cloaks cost $3(x-9.4)$ sickles. Since the friends bought three cloaks, spending all their money, we have $\frac{2}{3} x+\frac{3}{4} x+\frac{4}{5} x=3(x-9.4)$. Solving this equation, we get: $x=36$.

Grading criteria.

"+" A correct and justified solution and the correct answer are provided

“士” The equation is correctly and justifiedly formulated, but the solution is incomplete or contains a computational error

"耳" The correct answer is provided and it is shown that it satisfies the condition

“耳” Only the correct answer is provided

“-" An incorrect solution is provided or it is missing