Jen Butler has been pricing speed pass train fares for a group trip to new york. three adult and four children must pay $122. two adults and three children must pay $87. find the price of the adult ticket and the price of the child

Accepted Solution

Let price of adult ticket is $xAnd price of child ticket is $ySo 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 equationsMultiply 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= $18Price of child ticket = $17