Question

A high school is having a pancake breakfast fundraiser.They have 5 packages of pancake mix that each feed 140 people.The function N(p)=140p represents the number of people,N(P),that packages of pancake mix feed write the domain and range as compound inequalities.

Answer 1

They have 5 packages of pancake mix.

N(p) = 140*p

Represents the number of people that can be feed with p = # of packages of pancake mix used.

Now, the domain will be the set of the possible values of p that we can use here.

the set of possible values of p will be:

{0, 1, 2, 3, 4, 5}

We can not use more than 5 because there are only 5 packages.

But we can use actually half a package or a third, so we not should use only whole numbers in the domain, then the domain can be written as:

D = 0 ≤ p ≤ 5

Now, the range is the set of the possible values of N(p)

The minimum will be when p = 0.

N(0) = 140*0 = 0

The maximum will be when p = 5

N(5) = 140*5 = 700

Then the range can be written as:

R = 0 ≤ N ≤ 700

Here we could add another restriction, because we can only feed a whole number of people, then we also should add the restriction that N must be a whole number:

R = 0 ≤ N ≤ 700, N ∈ Z