Solve using two equations with two variables.?

Question

El Segundo High School put on their annunal musical. The studnets sold 650 tickets for value of $4375. if orchestra seats cost $7.50 and balcony seats costs $3.50, how many of each kind of seat were sold?

Answer 1

7.5x + 3.5y = 4375

x + y = 650

-3.5x - 3.5y = -2275

4x = 2100

x = 525

525 + y = 650

y = 125

Orchestra Seats = 525
Balcony Seats = 125

Answer 2

The key is the total number of tickets sold. (650)

So if X number of orchestra tickets are sold the remaining tickets have to be balcony seats.
# of Balcony seats = 650 - # of Orchestra seats

I get a formula of

3.5(650 -x) + 7.5x = 4375

2275 - 3.5x + 7.5x = 4375

4x = 2100

x = 525

So 525 Orchestra seats sold @ $7.50 ea = 3937.50
650 - 525 = 125
125 Balcony seats sold @ $3.50 ea = 437.50

Answer 3

Lets say the number of orchestra seats are "x" and the number of balcony seats are "y". The total number of seats are equal to the number of tickets selled, 650, and the total cost of the 650 seats is $4375.

Then: x + y = 650 (seats)
if $7.5 cost orchestra seats, and $3.5 cost balcony seats
7.5*x +3.5*y = 4375 (total cost)

So we have the sistem of two equations in to variables:

x + y = 650
7.5x + 3.5y = 4375

if we multiply the upper row by -3.5, we cancel the "y"

( x + y = 650 ) * 3.5
7.5x + 3.5y = 4375
------------------------------
-3.5x - 3.5y = -2275 (a)
7.5x + 3.5y = 4375 (b)

if we do a + b, obtain:

4x = 2100

resolving for x:

x = 2100/4

x= 525

so there are 525 balcony seats

and like x + y = 650:

650 - 525 = y = 125

there are 125 orchestra seats.

Answer 4

Set up two equations...

7.5 * x + 3.5 * y = 4375
x + y = 650

X is orchestra seats, and Y is balcony seats, so between the two, when multiplied by the price, they need to add up to the total money, and by themselves, they must add up to the number of tickets sold.

Then just solve by the elimination method. Do you know how?

Answer 5

let x = number of tickets sold for 3.50
then 650-x is the number of tickets sold for 7.50

(650 -x) 7.50 + 3.50x =4375
4875 -7.50x + 3.50x = 4375
4875 -4x = 4375
-4x = -500
x= 125 (sold for 3.50)

650-125 = 525 (sold for 7.50)

Answer 6

If he buys own homestead page x of the 4% and own homestead page y of the 6% then x+y=ten thousand The interest on the 4%=4percentof x=4x/a hundred, and on the 6% =6% of y =6y/a hundred so 4x/a hundred+6y/a hundred=500 giving 4x+6y=50000 you could divide this by ability of two giving 2x+3y=25000 and sparkling up this concurrently with x+y=ten thousand you will desire to get x=5000 and y=5000

Answer 7

This is the third one of this type you have asked....perhaps you should try them first?

I will give you the equations...but you need tosolve.

x + y =650
7.50x + 6.50y = 4375

where x is the number of adult tickets sold and y is the number of student tickets sold.

Answer 8

(x + y = 650
(7.50x + 3,50y = 4375