I was doing my homework and I came through this question. Can someone help?

Question

A movie theater charges $7 for adults, $5 for children under age 17 and $4 for seniors over age 60. For one showing of The Jungle Book, the theater sold 222 tickets and took in $1383. If twice as many adults tickets were sold as the total of children and senior tickets, how many tickets from each type were sold?

Answer 1

Let c = number children's tickets, and s = number of senior tickets

then, the number of adult tickets will equal 2(c + s)



Equation 1. 2(c + s) + c + s = 222

expanding, we get 3c + 3s = 222

solving for c, we get c = (222 - 3s)/3



Equation 2. $7a + $5c + $4s = $1383

but a = 2(c + s), so $7•2(c + s) + $5c + $4s = $1383

expanding, we get 14c + 14s + 5c + 4s = 1383

combining, we get 19c + 18s = 1383

solving for c, we get c = (1383 - 18s)/19



so from equation 1, c = (222 - 3s)/3, and from equation 2, c = (1383 - 18s)/19



we combine the two equalities to get (222 - 3s)/3 = (1383 - 18s)/19

we cross multiply to get 4218 - 57s = 4149 - 54s

solving, s = 23 tickets



we substitute that value into equation 1 to get 2(c + 23) + c + 23 = 222

solving for c, we get c = 51 tickets

therefore the number of adult tickets = 222 - 51 - 23 = 148

we see that 2(51 + 23) = 148



Proof: 148•$7 + 51•$5 + 23•$4 = $1383