Question

Anna is selling tickets to the school's gymnastics competition. On the first day, she sells 5 adult tickets and 6 child tickets for a total of $58.00. On the second day, she sells 8 adult tickets and 11 child tickets for a total of $97.00. Which system of linear equations can be used to determine the cost of each adult ticket (x) and each child ticket (y)?

Answer 1

The cost of each adult ticket is $11.43

The cost of each child ticket is $0.14

Step-by-step explanation:

Given,

• The cost of each adult ticket = x
• The cost of each child ticket = y

On the first day,

Anna sells 5 adult tickets and 6 child tickets for a total of $58.00.

⇒ 5x + 6y = 58  ----------(1)

On the second day,

she sells 8 adult tickets and 11 child tickets for a total of $97.00.

⇒ 8x + 11y = 97  ----------(2)

Solving the equations for x and y values :

Multiply eq (1) by 8,

Mu;tiply eq (2) by 5 and subtract it from eq (1),

  40x + 48y = 484

- (40x + 55y = 485)

         - 7y = - 1    

⇒ y = 1/7

⇒ y = 0.14

The cost of each child ticket is $0.14

Substitute y = 0.14 in eq (1),

⇒ 5x + 6(0.14) = 58

⇒ 5x + 0.84 = 58

⇒ 5x = 58 - 0.84

⇒ 5x = 57.16

⇒ x = 57.16 / 5

⇒ x = 11.43

The cost of each adult ticket is $11.43

Answer 2

Answer:

For USA TESTPrep A.) 5x + 6y = 58

8x + 11y = 97

x = adult ticket price; y = child ticket price

number of tickets(price of each) = total amount

first day total → 5x + 6y = 58

second day total → 8x + 11y = 97

Step-by-step explanation: