Question

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

Answer 1

Answer: There are 4 costumers in "Sushi Emperor" on Tuesday.

Step-by-step explanation:

Here, 15 regular rolls and 20 vegetarian rolls on Tuesday,

Hence, the total rolls = 15 + 20 = 35

Out of which each customer ate 2 regular rolls and 3 vegetarian rolls,

Let there are x costumers on Tuesday,

Therefore, the total rolls taken by x costumers = 2 x + 3 x = 5 x

Since, the uneaten rolls that remained = 4 regular rolls + 11 veg rolls = 15 rolls,

⇒ 5 x + 15 = 35

⇒ 5 x = 20

⇒ x = 4

Thus, On Tuesday there are 4 costumers.

Answer 2

Answer:

2 chefs and thirteen customers

Step-by-step explanation:

Let x represent the number of chefs and let y represent the number of customers. Since we have two unknowns, we need two equations to find them.

Let's use the given information in order to write two equations containing x and y. For instance, we are given that each chef prepared 15 regular rolls, each customer ate 2 regular rolls, and 4 regular rolls remained uneaten. How can we model this sentence algebraically?

The total number of regular rolls prepared by chefs can be modeled by 15x, and the total number of regular rolls eaten by customers can be modeled by 2y. The difference between these quantities is represented by the 4 regular uneaten rolls, which gives us the following equation:

15x-2y=4

We are also given that each chef prepared 20 vegetarian rolls, each customer ate 3 vegetarian rolls, and 1 vegetarian roll remained uneaten. This can be expressed as:

20x-3y=1

Now that we have a system of two equations, we can go ahead and solve it!  

We can now solve the system of equations by the elimination method. Let's manipulate the equations so one of the variables has the same coefficients but with opposite signs.

−4⋅15x−(−4)⋅2y

−60x+8y

​    

=−4⋅4

=−16

​  

3⋅20x−3⋅3y

60x−9y

​    

=3⋅1

=3

​  

Now we can eliminate x:

−60x+8y=-16

+ 60x−9y=3

-------------------

0-y=-13

When we solve the resulting equation, we obtain that y =13, equals, 13. Then, we can substitute this into one of the original equations and solve for x to obtain x=2, equals, 2.

Recall that x denotes the number of chefs and yyy denotes the number of customers. Therefore, there were 2 chefs and 13 customers.