Need help solving this please

Question

The cost of a ticket to the circus is $12.00 for children &$37.00 for adults. On a certain day attendance at the circus was 1900 and total gate revenue was $52,800. How many children and how many adults bought tickets?

Answer 1

Here's the substitution method;

c + a = 1900, so a = 1900 - c

12c + 37a = 52800

12c + 37(1900 - c) = 52800. Use distributive rule to eliminate parentheses.

12c + 70300 - 37c = 52800 Combine like terms, etc.

-25c = -17500

c = 700 children

So a = 1900 - 700 = 1,200 adults.

Answer 2

12c +37a = 52800

c + a = 1900

12c +12a = 12(1900)

25a = 52,800- 22,800

a = 30,000/25 = 1,200 adults

c =1900-1200 = 700 children

check the answers:

12(700)+37(1200)

=8400+ 44400

= 52800