Question

The student’s council is setting up a concession stand for a 24 hour relay. They plan on selling hot dogs hamburgers. A maximum of 600 hamburgers and hot dogs are needed. From the previous year’s relay the demand should be at least four times as many hot dogs as hamburgers

a) define the variables.
b) write a system of linear inequalities to represent this situation

Answer 1

Answer with explanation:

Maximum Number of hamburgers and Hot Dogs required for the Relay =600

Let number of Hamburgers =a

And Number of Hot dogs = b

So, In terms of Inequality, the above statement can be written as:

1.⇒ a+b ≤ 600

It is also given that, Demand of Hot Dogs should be at least four times as Hamburgers.

So,this statement in terms of Inequality can be written as:

⇒ Demand of Hot Dogs ≥ 4 × Demand of Hamburgers

2 ⇒ b ≥ 4 a

⇒Here,a and b are Variables Representing, number of Hamburgers ,and Number of Hot dogs Respectively.

And, the system of Linear inequalities representing this situation is

a+b ≤ 600

b ≥ 4 a

Answer 2

For this item, we let the number of hotdogs to be sold be x and that the number of hamburgers will be y. The system of linear inequality that would represent this scenario is,
x + y ≤ 600
x ≥ 4y