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At school Spencer is selling tickets to the Little Mermaid play. The first day of ticket sales sold 5 senior citizen tickets and 4 child tickets for a total of $22. The school took in $54 with 24 senior citizen tickets and 2 child tickets. Create a system of equations based on the problems and find the cost of child tickets and senior tickets.

Respuesta :

Answer:

Step-by-step explanation:

Let A be cost of adult ticket

Let C be cost of child ticket

5A + 4C = 22

A = (22 - 4C)/5

Β  Β  Β  Β  Β  Β  Β  Β  24A + 2C = 54

24((22 - 4C)/5) + 2C = 54

Β 105.6 - 19.2C + 2C = 54

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β - 17.2C = - 51.6

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  C = $3.00

A = (22 - 4(3))/5 = $2.00

Step-by-step explanation:

Let,

Senior tickets = x

Child tickets = y

In case 1

5x + 4y = 22 (1)

In case 2

24x + 2y = 54

On multiplying both sides by 2

48x + 4y = 108 (2)

On subtracting 1 and 2

48x + 4y - (5x + 4y) = 108 - 22

48x + 4y - 5x - 4y = 86

43x = 86

x = 86/43

x = 2

From 1

5(2) + 4y = 22

10 + 4y = 22

4y = 22 - 10

4y = 12

y = 12/4

y = 3

Hence,

Cost of 1 child ticket = $ 2

Cost of 1 adult ticket = $ 3

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