Step-by-step explanation:
let one number of adult ticket = x
let one number of student ticket= y
let one number of child ticket = z
Rachel paid $52 for two adult,two student,and one child tickets:
2x + 2y + z = $52 ....equation 1
RJ paid $56 for one adult two student and three child tickets:
x + 2y + 3z = $56 ....equation 2
Hong paid $44 for one adult and four child tickets:
x + 0y + 4z = $44 ....equation 3
Subtractequation 1 from 2:
x - 2x +2y -2y +3z -z = 56-52
-x +2z = 4 ....equation 4
Subtract equation 3 from 2
x - x +2y - 0y +3z -4z = 56-44
2y -z = 12 ....equation 5
From equation 4, let's make z the subject of formula so that we can insert the value in equation 3:
-x+2z = 4
2z = 4+x
z = (4+x)/2
Insert in equation 3
x + 4z = 44
x + 4((4+x)/2) = 44
x + 2(4+x) = 44
x + 8+2x = 44
3x + 8 = 44
3x = 44-8
x = 36/3
x = 12
insert