On opening night of the play "The Music Man" at the Lewiston Civic Theater, 946 tickets were sold. The total receipts for the performance was $10,588. Children tickets cost $10 apiece, adult tickets cost $14 aplece, and senior citizen tickets cost $6 apiece. If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 334, determine how many tickets of each typo were sold.

There were children tickets, adult tickets, and senior citizen tickets sold.

The number of tickets sold are

Children = 256

Adults = 486

senior citizen = 204

Step-by-step explanation:

let

x = children ticket  = $10 per piece

y = adult ticket = $14 per piece

z = senior citizen = $6 per piece

x + y + z = 946 ( total tickets sold ) ( 1 )

Total receipt for performance

10x + 14y + 6z = $10588   ( 2 )

since the combined number of children and Adult tickets exceeded twice the number of senior citizen tickets by 334

x + y - 2z = 334 ( 3 )

substract equation 3 from equation 1

3z = ( 946 - 334 ) = 612 therefore Z = 204

next we multiply equation (1) by 14

14x + 14y + 14z = 13244 ( 4 )

substract equation (2) from ( 4 )

4x + 8z = 2656

= 4x + 8(204) = 2656

= 4x = 2656 - 1632

therefore : x = 256

back to equation 1

256 + y + 204 = 946

y = 946 - ( 256 + 204 ) = 486

Hence the number of tickets sold are

Children = 256

Adults = 486

senior citizen = 204

there is no question content here, but you for the free points! : d