At the movie theater, child admission is $6.30 and adult admission is $9.70. On Saturday, 130 tickets were sold for a total sales of $1080.80. How many adult tickets were sold that day

Answer 1

6.3c + 9.7a = 1080.8

c+a = 130

multiply 2nd by 6.3 to get

6.3c +6.3a = 130(6.3) then subtract from 1st equation to eliminate 1 variable

3.4a = 1080.8- 819

a = 261.8/3.4 = 2618/34 = 1309/17 = 77 adults

c = 130-77 = 53 children

check the answers

6.3(57) + 9.7(77) = 1080.8

Answer 2

Let A = # of adult tickets sold

C = # children tickets sold

A + C = 130 (130 tickets in total).

Now realize that each adult ticket brings in $9.70. An expression that represents the total receipts brought in by adults is 9.70A.

Similarly for children the money brought in is represented by 6.30C.

So equation two is:

9.7A + 6.3C = 1080.8, or

97A + 63C = 10808

I would use the substitution method since it is easy to isolate a variable in the very 1st equation:

A + C = 130

C = 130 - A

Substitute 130 - A for C in the last equation:

97A + 63(130 - A) = 10808

97A + 8190 - 63A = 10808

34A = 10808 - 8190

34A = 2618

A = 2618/34 = 77

That is the answer to the question, but you can find C too:

C = 130 - 77 = 53

Check:

9.70(77) + 6.30(53) = $1080.80