Question

A local theatre sells out for their show. They sell all 500 tickets for a total purse of $7,920.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?

Answer 1

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220

Explanation:

A local theater sells out their show. They sell all 500 tickets for a total of $7920 .00 . The total number of ticket sold is 500.

let

Number of children ticket sold = a

Adult ticket sold = 3a

Student ticket sold = 500 - 3a - a = 500 - 4a

Total cost = 7920

7920 = 12(a) + 15(500 - 4a) + 18(3a)

7920 = 12a + 7500 - 60a + 54a

collect like terms

7920 = 12a - 60a + 54a + 7500

7920 - 7500 = 6a

420 = 6a

divide both sides by 6

a = 420/6

a = 70

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220