SOLUTION: El Segundo High School put on their annual musical. the students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: El Segundo High School put on their annual musical. the students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each      Log On


   

Question 118007: El Segundo High School put on their annual musical. the students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?
Found 3 solutions by misscrt, MathLover1, stanbon:
Answer by misscrt(37) About Me  (Show Source):
You can put this solution on YOUR website!
El Segundo High School put on their annual musical. the students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?
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Let X= # of orchestra seats
Y= # of balcony seats
X+Y = 650 (Equation 1)
Next, write an equation for the cost of the seats...You were given that the total value of tickets sold was $4375.
So, the second equation will be:
7.50X + 3.50Y = 4375 (Equation 2)
Solve (1) for X:

X = 650-Y (Equation 3)
Plug this expression into (2) and solve for Y:
7.50(650-Y) + 3.50Y = 4375
4875 - 7.50Y + 3.50Y = 4375
4875 - 4.00Y = 4375
4875 -4875 -4.00Y = 4375 -4875
-4.00Y = -400
Y = -400/-4.00
Y= 100
There were 100 balcony seats sold. To find the number of orchestra seats sold simply use equation 3:
X = 650-100 = 550
Hope this helps.
Greetings,
misscrt

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sold S+=650+tickets
a value V=4375}$
If orchestra+seatsOs=7.50$
balcony+seats Bs=%24+3.50$
then:
650+=+Os%2BBs……………….(1)
4375=+Os%287.50%29+%2B+Bs%283.50%29…………(2)
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Os+=+%28+650+-+Bs%29+………..(1)…substitute it into (2)

4375+=+%28+650+-+Bs%29+%287.50%29%2B+Bs+%283.50%29+…………(2)
4375+=+%28+650+-+Bs%29+%287.50%29+%2B+Bs+%283.50%29+………
4375+=+%28+650+-+Bs%29+%287.50%29+%2B+Bs+%283.50%29+………
4375+=+4875+%96+%287.50%29Bs%2B+%283.50%29Bs+++………
4375+=+4875+%96+4Bs+………
+4B_s+=+4875+%96+4375……… divide both sides by 4
+Bs++=+1218.75+%96+1093.75………
+Bs+=+125++……tickets…....now substitute iy in (1) to solve for O_s

650+=+Os%2B125+……………….(1)
650+-+125+=+Os+………………
525++=+Os+………………tickets
Check a value:
4375=+525+%287.50%29+%2B+125%283.50%29…………(2)
4375=+3937.5%2B+437.5…………
4375=+4375…………

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
El Segundo High School put on their annual musical. the students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?
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Let # of orchestra tickets be "r"; Let # of balcony tickets be "b".
EQUATIONS:
Quantity: r+b=650
Value: 7.5r + 3.5b = 4375
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Substitute to solve for "b"
7.5(650-b) + 3.5b = 4375
4875-7.5b+3.5b = 4375
-4b = -500
b = 125 (# of balconey tickets sold)
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Substitute to solve for "r":
r+125 = 650
r = 525 (# of orchestra tickets sold)
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Cheers,
Stan H.