Questions on Algebra: Systems of Linear Equations answered by real tutors!

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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.: 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.
Answer by Fombitz(1755) About Me  (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.A+S=1800
"for a total of $12750"
2.8A+5S=12750
b.) Solve eq. 1 for A in terms of S.
1.A+S=1800
A=1800-S
Now substitute this expression into eq. 2 and solve for S,
2.8A+5S=12750
8(1800-S)+5S=12750
14400-8S+5S=12750
-3S=-1650
S=550
From above,
A=1800-S
A=1800-550
A=1250
There were 1250 adult tickets sold and 550 student tickets sold.
d.)
1.A+S=1800
1.1250+550=1800
1.1800=1800
True.
2.8A+5S=12750
2.8(1250)+5(550)=12750
2.10000+2750=12750
2.12750=12750
True.
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.: 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.
Answer by jim_thompson5910(9373) About Me  (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 x+y=1800. Also, because the prices were "$8 for adults, $5 for students" which gave them "a total of $12 750", this means that 8x+5y=12750

So we have the system:

system(x+y=1800,8x+5y=12750)


------------------

b)



Start with the given system of equations:
system(x+y=1800,8x+5y=12750)


-8(x+y)=-8(1800) Multiply the both sides of the first equation by -8.


-8x-8y=-14400 Distribute and multiply.


So we have the new system of equations:
system(-8x-8y=-14400,8x+5y=12750)


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


(-8x-8y)+(8x+5y)=(-14400)+(12750)


(-8x+8x)+(-8y+5y)=-14400+12750 Group like terms.


0x+-3y=-1650 Combine like terms. Notice how the x terms cancel out.


-3y=-1650 Simplify.


y=(-1650)/(-3) Divide both sides by -3 to isolate y.


y=550 Reduce.


------------------------------------------------------------------


-8x-8y=-14400 Now go back to the first equation.


-8x-8(550)=-14400 Plug in y=550.


-8x-4400=-14400 Multiply.


-8x=-14400+4400 Add 4400 to both sides.


-8x=-10000 Combine like terms on the right side.


x=(-10000)/(-8) Divide both sides by -8 to isolate x.


x=1250 Reduce.


So our answer is x=1250 and y=550.


-----------------------------------
c)
Since x=1250 and y=550, this means that there were 1,250 adults and 550 students.


-----------------------------------
d)

Check:

Let's check the first equation


x+y=1800 Start with the first equation.


1250+550=1800 Plug in x=1250 and y=550.


1800=1800 Add. Since this equation is true, this means that x=1250 and y=550 are solutions to the equation.


Now let's check the second equation


8x+5y=12750 Start with the second equation.


8*(1250)+5*(550)=12750 Plug in x=1250 and y=550.


10000+2750=12750 Multiply


12750=12750 Add. Since this equation is true, this means that x=1250 and y=550 are solutions to the equation.


Since both equations of the system are true, this verifies our answer.