The Little Town Arts Center charges 24 for adults 13 for sen

The Little Town Arts Center charges $24 for adults, $13 for senior citizens, and $9 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12, 903 for 854 tickets sold. There were 45 more children than adults. How many children attended?

Solution

Ticket charge

for adult = 24

for senior citizen = 13

for children = 9

Suppose number of adults = x

number of senior citizen = y

then number of children = x + 45

given that

x + y + x + 45 = 854

2x + y = 809

y = 809 - 2x

Also,

x*24 + y*13 + (x + 45)*9 = 12903

24x + 13y + 9x + 405 = 12903

33x + 13y = 12498

Since y = 809 - 2x

33x + 13*(809 - 2x) = 12498

33x - 26x + 13*809 = 12498

7x = 12498 - 809*13

7x = 1981

x = 253

Then number of children will be = x +45 = 253 + 45 = 298