Adult tickets to space city amusement park cost x dollars. Childrens tickets cost y dollars. The henson family bought 3 adult and 1 child ticket for $163. The Garcia family bought 2 adult and 3 child tickets for $174. Write equations to represent the Henson's cost and the Garcia's cost. Solve the system.

Henson family
[tex]3x + y = 163[/tex]

Garcia family
[tex]2x + 3y = 174[/tex]

Solution:

[tex]y = 163 - 3x[/tex]
Substitute that into
[tex]2x + 3(163 - 3x) = 174 \\ 2x + 489 - 9x = 174 \\ 7x = 315 \\ x = 45[/tex]

Substitute that into
[tex]y = 163 - 3(45) \\ y = 28[/tex]

Answer: x = 45, y = 28

Hope this helps. - M