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inna [77]
3 years ago
15

A family bought a total of 16 adult and child tickets to a magic show.adult tickets are 10.50 each and child tickets are 7.50 ea

ch .the family paid a total of $141
Mathematics
1 answer:
olga55 [171]3 years ago
4 0

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:

x+y=16         [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:

total\ paid = 10.50*x+7.50*y

We are given this total, thus

10.50*x+7.50*y=141            [2]

The system formed by [1] and [2] must be solved to answer the question. Let's solve [1] for x:

x=16-y

And substitute x in [2]:

10.50*(16-y)+7.50*y=141

Operating:

10.50*16-10.50*y+7.50*y=141

-10.50*y+7.50*y=141-10.50*16

Joining like terms and operating on the right side:

-3y=-27

Solving:

\displaystyle y=\frac{-27}{-3}

\boxed{y=9}

The value of x is calculated by

x=16-y=16-9

\boxed{x=7}

This means there were 7 adults and 9 children paying tickets to the magic show

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