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Answer:
<em>There were 7 adults and 9 children paying tickets to the magic show</em>
Step-by-step explanation:
<u>System of Equations</u>
A system of equations consists of more than one variable related to more than one equation. The question we're working on requires to know two variables: the number of children and the number of adults that paid to a magic show.
Let's call x to the number of adults and y to the number of children. The first condition states there are a total of 16 persons in the group. This can be written as:
[1]
We also know the adult tickets cost $10.50 each and child tickets cost $7.50 each. This means the total amount paid for the tickets is:
We are given this total, thus
[2]
The system formed by [1] and [2] must be solved to answer the question. Let's solve [1] for x:
And substitute x in [2]:
Operating:
Joining like terms and operating on the right side:
Solving:
The value of x is calculated by
x=16-y=16-9
This means there were 7 adults and 9 children paying tickets to the magic show