Question

Each chef at "Sushi Emperor" prepares 15 1515 regular rolls and 20 2020 vegetarian rolls daily. On Tuesday, each customer ate 2 22 regular rolls and 3 33 vegetarian rolls. By the end of the day, 4 44 regular rolls and 1 11 vegetarian roll remained uneaten. How many chefs and how many customers were in "Sushi Emperor" on Tuesday?

Answer 1

Answer:

• 2 chefs and 13 customers

Step-by-step explanation:

Let the number of chefs is x and the number of customers is y.

Regular rolls

• Prepared 15x, eaten 2y, left 4

Equation:

• 15x = 2y + 4          >>> (1)

Vegetarian rolls

• Prepared 20x, eaten 3y, left 1

Equation:

• 20x = 3y + 1          >>> (2)

We have a system.

Solve it by elimination, multiply the first one by 4 and the second one by 3:

• 15x*4 = 2y*4 + 4*4 ⇒ 60x = 8y + 16
• 20x*3 = 3y*3 + 1*3 ⇒ 60x = 9y + 3

Compare the equations:

• 8y + 16 = 9y + 3
• 9y - 8y = 16 - 3
• y = 13

Substitute the value of y into first equation and solve for x:

• 15x = 2*13 + 4
• 15x = 30
• x = 2