Use a system to model each situation. Solve by using the elimination or substitution method?

Question

A family goes to a school play. 2 adult tickets and 2 student tickets cost $9.50. Another family needs 2 adult tickets and 3 student tickets. Their total cost was $11.25. Find the price of each ticket.

Answer 1

Let x = price of adult ticket
Let y = price of student ticket

2x + 2y = 9.5
2x + 3y = 11.25

-1(2x + 2y = 9.5)
-2x - 2y = -9.5
2x + 3y = 11.25
----------------------
y = 1.75

2x + 2(1.75) = 9.5
2x + 3.5 = 9.5
2x = 6
x = 3

Adult tickets are $3.00 and student tickets are $1.75.

Answer 2

Let

a = adults tickets

s = students tickets

2a + 2s = 9.50- - - - - -Equation 1
2a + 3s = 11.25- - - - -Equation 2
- - - - - - - - - - - -
Multiply equation 1 by -1

2a + 2s = 9.50

- 1(2a) + (- 1)(2s) = - 1( 9.50)

- 2a + (- 2s) = - 9.50

- 2a - 2s = - 9.50

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

- 2a - 2s = - 9.50
2a + 3s = 11.25
- - - - - - - - - - - -

s = 1.75

Insert the s value into equation 1

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

2a + 2s = 9.50

2a + 2(1.75) = 9.50

2a + 3.50 = 9.50

2a + 3.50 - 3.50 = 9.50 - 3.50

2a = 6

2a / 2 = 6 / 2

a = 6 / 2

a = 3

Insert the a value into equation 1

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

Check for eqution 1

2a + 2s = 9.50

2(3) + 2(1.75) = 9.50

6 + 3.50 = 9.50

9.50 = 9.50

- - - - - - - - - - -

Check for equation 2

2a + 3s = 11.25

2(3) + 3(1.75) = 11.25

6 + 5.25 = 11.25

11.25 = 11.25

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

Both equations balance

The Price for the adults tickets is $ 3.00

The price for the students tickets is $ 1.75

- - - - - - - - -s-

Answer 3

a = adult tickets
s = student tickets

2a + 2s = 9.50
2a + 3s = 11.25

elimination:
-2a - 2s = -9.50
2a + 3s = 11.25

s = 1.75

2a + 2(1.75) = 9.50
2a + 3.50 = 9.50
2a = 6
a = 3

Answer 4

Let H = price of a hotdiggitydog and F= price of an order of fries #1] 3H + 2F = 8.50 #2] 2H + F = 5.25 Multiply equation #2 by -2 and then add it to equation #1 3H + 2F = 8.50 -4H - 2F = -10.5 -H = -2 H = 2 Substitute this back into one of your equations. I will use #2: 2(2) + F = 5.25 4 + F = 5.25 F = 1.25 Therefore, a hotdiggitydog costs $2 and fries cost $1.25

Answer 5

a = adult ticket
s = student ticket
2a + 2s = 9.50
2a + 3s = 11.25
use elimination since the coeffient of both a's match.
2a + 2s = 9.50
- 2a - 3s = -11.25
______________
-s = -1.75
s = $1.75
plug in s in either equation:
2a + 2(1.75) = 9.5
a = $3.00

Answer 6

11.25-9.50=student ticket=1.75
so
9.50-(2 * 1.75)
---------------------=adult ticket
2


system
2 st + 2 at=9.5 => -2 st - 2 at= -9.5
2 st+ 3 at=11.25 => same
-----------------------------------------------------------add
at=11.25-9.5
=> sub in first st

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