Question

Adult tickets to space city amusement park cost x dollars. children's tickets cost y dollars. the garcia family bought 3 adult and 1 child ticket for $164. the henson family bought 2 adult and 3 children's tickets for $174

Answer 1

A childs ticket = $28 and an adult = $45 
Total Cost to each family is the number of adult tickets bought multiplied by "x" PLUS the number of child tickets bought multiplied by "y" 
Henson's equation = 3x + y = 163 Garcia's equation = 2x + 3y = 174 
using the substitution method we need to express either x or y in terms of the other variable. In this example looking at the Henson equation it is very easy to express y in terms of x. 
Rewrite the Henson equation to make y the subject y = 163 - 3x Substitute this value (163 - 3x) for "y" in the Garcia equation which now becomes 
2x + 3(163 - 3x) = 174 Expand the bracket 2x + 489 - 9x = 174 -7x + 489 = 174 Add 7x and subtract 174 from both sides of the equation 315 = 7x 315/7 = x 45 = x An adult ticket costs $45 Substitute this back into the Henson equation 3 * 45 + y = 163 135 + y = 163 y = 163 - 135 = 28 A childs ticket costs $28 
Check in the Garcia equation 2 * 45 + 3 * 28 = 90 + 84 = 174 = CORRECT 
A childs ticket = $28 and an adult = $45