Question

Two groups of people went to see Iron Man 3

in IMAX 3-D. The first group spent $73.50 on
two adult and three children tickets. The other
group spent $109.50 on five adult and two
children tickets. What is the cost of one adult
ticket?

Answer 1

Answer:Answer: An adult’s ticket costs $9 while a children’s ticket costs $5.

Explanation:

1). 2x + 3y = 33

2). 5x + 2y = 55

3). I’m going to use substitution.

Isolate a variable (x):

2x + 3y = 33

2x = -3y + 33

X = (-3y + 33)/2

X = -3/2y + 33/2

Substitute and solve for y:

5x + 2y = 55

5(-3/2y + 33/2) + 2y = 55

-15/2y + 165/2 + 2y = 55

-11/2y = -55/2

Y = 5 <— children’s ticket.

Solve for x:

2x + 3y = 33

2x + 3(5) = 33

2x + 15 = 33

2x = 18

X = 9 <— adult’s ticket.

Check:

5x + 2y = 55

5(9) + 2(5) = 55

45 + 10 = 55

55 = 55

2x + 3y = 33

2(9) + 3(5) = 33

18 + 15 = 33

33 = 33

Explanation:

Answer 2

x = 16.5

Explanation:

2x + 3y = 73.50

5x + 2y = 109.50

(2x + 3y = 73.5) -5

(5x + 2y = 109.5) 2

-10x - 15y = -367.5

10x + 4y =219

-11y = -148.5

y = 13.5

2x + 3(13.5) = 73.50

2x + 40.5 = 73.5

2x = 73.5 - 40.5

2x = 33

x = 16.5