The admission at the movies is $5 for children and $10 for adults. The total amount collected was $3,000.00. There was a total of 500 people. Create a system of linear equations to figure out how
many of the people were children and how many were adults.

Number of children, x= 400

Number of adults, y = 100

Step-by-step explanation:

Let the number of children be x

Let the number of  adults be y

Given : Total number of people,  x + y = 500  (1)

           Total amount collected, 5x + 10y = 3000  (2)

(1) => y = 500 - x

Substitute y in (2) : 5x + 10(500 - x) = 3000

                             5x + 5000 - 10x = 3000

                                -5x = 3000 - 5000

                                 -5x = -2000

                                    x = 400

Substitute x in (1) : 400 + y = 500

                                      y = 500 - 400

                                      y = 100

23,598 because  513 x 40 = ( 500 x 40 ) + ( 10 X 40 ) + ( 3 x 40 ) = 20 000 + 400 + 120 = 20,520 and another partial product is  513 x 6 = ( 500 x 6 ) + ( 10 x 6 ) + ( 3 x 6 ) = 3 000 + 60 + 18 = 3,078. so 20,520 + 3,078 = 23,598