Alocal movie theater charges $12 for an adult ticket and $10 for a child’s ticket. a group of eight people spent a total of $86 on tickets to a movie. how many adults and how many children were in the group? a. write a system of linear equations based on the description. use x to represent the number of adults and y to represent the number of children. b. solve the system using the elimination method. show all the steps leading to your answer. c. write 1-2 sentences to explain what the solution means for this situation.

Number of adult tickets = 3 tickets

Number of children tickets = 5 tickets

Step-by-step explanation:

A- The system of equations:

Assume that the number of adult tickets is x and that the number of children tickets is y

We are given that:

i. The total number of people in the group is 8, which means that the total number of tickets bought is 8. This means that:

x + y = 8 > equation I

ii. The price of an adult ticket is $12 and that of a child ticket is $10. We know that the group spent a total of $86. This means that:

12x + 10y = 86 > equation II

From the above, the systems of equation is:

x + y = 8

12x + 10y = 86

B- Solving the system using elimination method:

Start by multiplying equation I by -10

This gives us:

-10x - 10y = -80 > equation III

Now, taking a look at equations II and III, we can note that coefficients of the y have equal values and different signs.

Therefore, we will add equations II and III to eliminate the y

    12x + 10y = 86

+( -10x - 10y = -80)

Adding the two equations, we get:

2x = 6

x = 3

Finally, substitute with x in equation I to get the value of y:

x + y = 8

3 + y = 8

y = 8 - 3 = 5

Based on the above:

Number of adult tickets = x = 3 tickets

Number of children tickets = y = 5 tickets

C- Explanation of the meaning of the solution:

The above solution means that for a group of 8 people to be able to spend $86 in a theater having the price of $12 for an adult ticket and $10 for a child' one, this group must be composed of 3 adults and 5 children

Hope this helps :)