202 tickets are sold. a child costs $6 and an adult ticket costs $10. How may tickets of each were sold if the receipts totaled $1708?

The number of child tickets = 78 and the number of adult tickets = 124

Step-by-step explanation:

Let the number of child ticket is x and the adult ticket is y

∴ x + y = 202 ⇒ (1)

∵ The cost of child ticket is $6 and adult ticket is $10

∴ 6x + 10 y = 1708 ⇒ (2)

Solve the system of equations (1) and (2)

Multiply (1) by - 6 to eliminate x

∴ - 6x + - 6y = - 1212 ⇒ (3)

Add (2) and (3)

∴ 4y = 496

∴ y = 124

Substitute the value of y in (1)

∴ x + 124 = 202 ⇒ x = 202 - 124 = 78

∴ The number of child tickets = 78 and the number of adult tickets = 124