Question

Each chef at "Sushi Emperor" prepares
\[15\] regular rolls and
\[20\] vegetarian rolls daily. On Tuesday, each customer ate
\[2\] regular rolls and
\[3\] vegetarian rolls. By the end of the day,
\[4\] regular rolls and
\[1\] vegetarian roll remained uneaten.
How many chefs and how many customers were in "Sushi Emperor" on Tuesday?

Answer 1

Let c = number of chefs and n = number of customers.

Regular: 15c produced, 2n eaten, 4 left → 2n = 15c − 4.
Vegetarian: 20c produced, 3n eaten, 1 left → 3n = 20c − 1.

Solve:
From 2n = 15c − 4 and 3n = 20c − 1, multiply the first by 3 and the second by 2:
6n = 45c − 12
6n = 40c − 2
Equate: 45c − 12 = 40c − 2 → 5c = 10 → c = 2.
Then 2n = 15·2 − 4 = 26 → n = 13.

Answer: 2 chefs and 13 customers.