Solve this application problem using a system of equations: The Springfield Movie Theater sold adult tickets for $4.10 each and children's tickets for $2.70 each. Last Thursday, a total of $331.30 was collected from 89 movie watchers. How many of each type of ticket were sold on Thursday?

Answer: 65 adult ticket and 24 children's ticket

Step-by-step explanation:

Let the total number of adults be x

And the total number of children be y

The cost of ticket for 1 adult = $4.10, this means that the cost of ticket for x adults will be 4.10x

The cost of ticket for a child = $2.70, this means that the cost of ticket for y children will be 2.70y.

The total sale was $331.30, that is

4.10x + 2.70y = 331.30

Total number of movie watchers were 89, that is

x + y = 89

Combining the two equations, we have:

x + y = 89 ... equation 1

4.10x + 2.70y = 331.30 ... equation 2

solving the system of linear equation by substitution method.

From equation 1, make x the subject of the formula

x = 89 - y ... equation 3

substitute x = 89 - y into equation 2, equation 2 then becomes

4.10 (89 - y) + 2.70y = 331.30

expanding the bracket, we have

364.9 - 4.10y + 2.70y = 331.30

364.9 - 1.4y = 331.30

collecting the like terms, we have

364.9 - 331.30 = 1.4y

33.6 = 1.4y

divide through by 1.4

33.6/1.4 = y

Therefore : y = 24

substitute y = 24 into equation 3

x = 89 - y

x = 89 - 24

x = 65

Therefore, there were 65 adults and 24 children ticket sold