Answered

a restaurant offers three desserts, and exactly twice as many appetizers as main courses. a dinner consists of an appetizer, a main course, and a dessert. what is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003?



Answer :

tutorconsortium270

The least number of main courses that the restaurant should offer is 8.

What is linear inequality ?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

Calculations

let m be  the number of main courses restaurant serves

so, 2m is the number of appetizers  

then the number of dinner combination is =  2m x m x 3 = 6m^2

since the customer wants to eat a different dinner in all 365 days of 2003,

we must have ,

[tex]6m^{2}[/tex] ≥  365

[tex]m^{2}[/tex]  ≥ 60.83.....

also the 2003 is not a leap year

because 2003 / 4 is not equal to an integer

the smallest integer value satisfies this is 8 .

learn more about the linear inequalities here :

brainly.com/question/19526736

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