You can
put this solution on YOUR website!Let x=# of adults and y=# of students
Since the "63 tickets were sold", this means that the first equation is
Also, because the tickets "were sold at $6 for adults and $4.50 for students" and they collected a "total of $358.50", this means that the second equation is
Multiply every term in the second equation by 10 to move the decimal point one spot to the right
So we have the system of equations:
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
Subtract
from both sides
Rearrange the equation
---------------------
Since
, we can now replace each
in the second equation with
to solve for
Plug in
into the first equation. In other words, replace each
with
. Notice we've eliminated the
variables. So we now have a simple equation with one unknown.
Distribute
to
Multiply
Combine like terms on the left side
Subtract 2835 from both sides
Combine like terms on the right side
Divide both sides by 15 to isolate x
Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that
we can plug it into the equation
(remember we previously solved for
in the first equation).
Start with the equation where
was previously isolated.
Plug in
Multiply
Combine like terms
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
So there were 50 adults and 13 students
