I need help please to solve this

Question

The cost of a ticket to the circus is $22 for children and $42 for adults on a certain day attendance at the circus was 1900 and the total gate revenue was 63,800 how many children and how many adults bought tickets?

Answer 1

Let A be the number of adult tickets, C be the number of children tickets. Then the following equations result:

A+C = 1900 [1] and

42A+22C = 63800 [2].

Solve [1]: C = 1900-A . Substitute for C in [2]: 42A + 22(1900-A) = 63800.

Solve for A: 42A+(22)(1900)-22A = 63800

42A - 22A = 63000 - (22)(1900)

20A = 63800-41800 = 22000

A = 22000/20 = 1100, which gives C = 1900-1100 = 800

Check solution: (100)(42) + (800)(22) = 63800.

Answer 2

Let x = number of children, then 1900 - x = number of adults

22x + 42(1900 - x) = 63800

Solve for x.