Question

Can someone help me with System of Equations? Plz show ur work for the 3 answers plz

{answer 1: $1 child
$7.25 adult {answer 2) $1 child
$6.50adults
{answer 3) $2 child
$4.50 adult

A school play sells adult and child tickets. On Friday they sold 55 child tickets and 20 adult tickets for $200. On Saturday they sold 72 child tickets and 36 adult tickets for $306. What is the cost of each individual ticket?

Answer 1

Let's make the price of tickets for adults x and children y, now form an equation
Friday - 55y + 20x = 200
Saturday - 72y + 36x = 306
Now you have to have either the x or the y cancel out, so you have to find the relationship between two of them
I am going to multiply the top equation by 9/5 to cancel out the x
99y + 36x = 360
72y + 36x = 306
Now I am going to multiply the bottom equation by -1
-72y - 36x = -306
99y + 36x = 360
The x cancel out
27y = 54
y = 2
So the price of a child ticket is $2
Now plug 2 into one of the original equations
55(2) + 20x = 200
20x = 90
x = 4.5
The price of an adult ticket is $4.50