Let price of adult ticket is $x
And price of child ticket is $y
So we can make two equations using the given data
[tex] 3x+4y = 122 [/tex]
[tex] 2x+3y = 87 [/tex]
Now we can use eliminator method to solve the two equations
Multiply first equation by 2 and second equation by -3
[tex] 2(3x+4y = 122) [/tex]
[tex] -3(2x+3y = 87) [/tex]
[tex] 6x+8y = 244 [/tex]
[tex] -6x-9y =-261 [/tex]
now add both the equations so we get
[tex] 6x-6x+8y-9y=244-261 [/tex]
combine the like terms
[tex] -y=-17 [/tex]
Divide both sides by -1
[tex] y=17 [/tex]
Plug y=17 in any one of the equations to solve for x
[tex] 3x+4(17) = 122 [/tex]
[tex] 3x+68 = 122 [/tex]
Subtract 68 from both sides
[tex] 3x = 54 [/tex]
Divide both sides by 3
[tex] x=18 [/tex]
So x=18 and y=17
So
Price of adult ticket= $18
Price of child ticket = $17
