Question

What is the solution to the system? For the first tour on Monday, a museum sells 6 child tickets and 8 adult tickets for $140. For the second tour, the museum sells 12 child tickets and 9 adult tickets for $189. Find the price of one child ticket and the price of one adult ticket.

Answer 1

children = $6 ; adults = $13

Explanation:

6c + 8a = 140

12c + 9a = 189

3c + 4a = 70

4c + 3a = 63

3c = 70 - 4a

c = 70/3 - 4/3 a

4(70/3 - 4/3 a) + 3a = 63

280/3 - 16/3 a + 3a = 63

(-16a + 9a)/3 = 63 - 280/3

-7/3 a = (189 -280)/3

-7/3 a = -91/3

a = - 91/3 · -3/7

a = 91/7

a = $13

c = 70/3 - 4/3 · 13

c = 70/3 - 52/3

c = (70-52)/3

c = 18/3

c = $6