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
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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) (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?
_______________________________________________________________________
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 $4375.
So, the second equation will be:
7.50X + 3.50Y = 4375 (Equation 2)
Solve (1) for X:
X = 650-Y (Equation 3)
Plug this expression into (2) and solve for Y:
7.50(650-Y) + 3.50Y = 4375
4875 - 7.50Y + 3.50Y = 4375
4875 - 4.00Y = 4375
4875 -4875 -4.00Y = 4375 -4875
-4.00Y = -400
Y = -400/-4.00
Y= 100
There were 100 balcony seats sold. To find the number of orchestra seats sold simply use equation 3:
X = 650-100 = 550
Hope this helps.
Greetings,
misscrt
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
sold
a value }$
If seats$
seats $
then:
.(1)
(2)
------------------------------------------------------------------
..(1)
substitute it into (2)
(2)
divide both sides by
tickets
....now substitute iy in (1) to solve for
.(1)
tickets
Check a value:
(2)
Answer by stanbon(75887) (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?
-----------------
Let # of orchestra tickets be "r"; Let # of balcony tickets be "b".
EQUATIONS:
Quantity: r+b=650
Value: 7.5r + 3.5b = 4375
-------------------
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)
--------
Substitute to solve for "r":
r+125 = 650
r = 525 (# of orchestra tickets sold)
=================
Cheers,
Stan H.
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