Atheater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. at a certain screening with fll ttendance, there were combined. the receipts totaled $3450. how many children attended the show?

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving  a system of linear equations.

First we write the system equations :

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

This equation represents the totaled receipts.

The system :

has the following associated matrix :

By performing elementary matrix operations we find that the matrix is equivalent to

The new system :

Working with the equations :

Our solution vector is :

For example :

If 0 adults attended ⇒ A = 0

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)