SOLUTION: MY LAST MODULE QUESTION!!! YAYA! but i cant figues it out .... Help please?? q: A concert promoter set the following ticket prices: $8 for adults, $5 for students. There were 18

Question 152717: MY LAST MODULE QUESTION!!! YAYA! but i cant figues it out ....
Help please??
q: A concert promoter set the following ticket prices: $8 for adults, $5 for students. There were 1800 tickets sold for a total of $12 750.
a. Write a system of equations in two variables to model the situation.
b. solve the system of equations.
c.indicate the number of adult tickets and student tickets sold.
d. check that your answer fits the equation.
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) (Show Source): 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.
Answer by jim_thompson5910(35256) (Show Source): 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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