You can
put this solution on YOUR website!Let A be the number of adult tickets at $8 each.
Let S be the number of student tickets at $5 each.
a.)
"1800 total tickets sold"
1.
"for a total of $12750"
2.
b.) Solve eq. 1 for A in terms of S.
1.
Now substitute this expression into eq. 2 and solve for S,
2.
From above,
There were 1250 adult tickets sold and 550 student tickets sold.
d.)
1.
1.
1.
True.
2.
2.
2.
2.
True.
You can
put this solution on YOUR website!a)
Let x=# of adults and y=# of students
Since "There were 1800 tickets sold", this means that
. Also, because the prices were "$8 for adults, $5 for students" which gave them "a total of $12 750", this means that
So we have the system:
------------------
b)
Start with the given system of equations:
Multiply the both sides of the first equation by -8.
Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms. Notice how the x terms cancel out.
Simplify.
Divide both sides by
to isolate
.
Reduce.
------------------------------------------------------------------
Now go back to the first equation.
Plug in
.
Multiply.
Add
to both sides.
Combine like terms on the right side.
Divide both sides by
to isolate
.
Reduce.
So our answer is
and
.
-----------------------------------
c)
Since
and
, this means that there were 1,250 adults and 550 students.
-----------------------------------
d)
Check:
Let's check the first equation
Start with the first equation.
Plug in
and
.
Add. Since this equation is true, this means that
and
are solutions to the equation.
Now let's check the second equation
Start with the second equation.
Plug in
and
.
Multiply
Add. Since this equation is true, this means that
and
are solutions to the equation.
Since
both equations of the system are true, this verifies our answer.
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