Answer: (5,8)
Step-by-step explanation:
So this is a matter of using a system of linear equations
To start if a total of 13 people got a ticket then we know that
x+y=13
x and y being explained in the problem
then if adult tickets are $40 and children tickets are $20 and the total cost is 360 we can set up the next equation
40x+20y=360
<em>If you were to plug in 1 lets say into x that means that 1 person bought a ticket for $40 this shown by 40 (1) this is the same premise for the childrens tickets.</em>
now we have
x+y=13
40x+20y=360
now we can solve by eliminating one of the variables this is done by either getting rid of the x or y and solving for the other. I solved for the y value first this looks like
-40(x+y=13)
40x+20y=360
Distribute the -40 to each value
giving you
-40x-40y=-520
40x+20y=360
add these together from the top down
the x's cancel leaving
-20y=-160
then isolate the y value by dividing both sides by -20
-20y/-20=-160/-20
leaving you with your y point
y=8
This is how many childrens rickets were sold now we can plug into the first linear equation
x+8=13
now easy subtration to isolate the x point
x+8-8=13-8
x=5
Finally leaving you with point (5,8)
