Question

Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. on tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?

Answer 1

Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.

1. If each chef prepares 15 regular rolls, then x chefs prepar 15x regular rolls. If each customer ate 2 regular rolls, then y customers ate 2y regular rolls. By the end of the day, 4 regular rolls remained uneating. This means that the amount of prepared rolls is greater than amount of eaten rolls by 4:

15x-2y=4.

2. If each chef prepares 20 vegetarian rolls, then x chefs prepar 20x vegetarian rolls. If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls. By the end of the day, 1 vegetarian roll remained uneating. This means that the amount of prepared rolls is greater than amount of eaten rolls by 1:

20x-3y=1.

3. Solve the system of equations:

$\left\{\begin{array}{l}15x-2y=4\\20x-3y=1.\end{array}\right.$

From the first equation $y=7.5x-2.$ Substitute it into the second equation:

$20x-3(7.5x-2)=1,\\ \\20x-22.5x+6=1,\\ \\-2.5x=-5,\\ \\x=2.$

Then

$y=7.5\cdot 2-215-2=13.$

Answer: 2 chefs and 13 customers.

Answer 2

Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday. The equations that would best represent the scenario above using the number of items uneaten are:
        (regular rolls):       15x - 2y = 4
        (vegetarian rolls):   20x - 3y = 1
The values of x and y from the system of linear equations are:
                            x = 2 and y = 13
Therefore, there were 2 chefs and 13 customers.