At an amusement park, the cost of 3 adult tickets and 4 children’s tickets is 126.50. Another customer paid 120.50 for 2 adult tickets and 5

Question

At an amusement park, the cost of 3 adult tickets and 4 children’s tickets is 126.50. Another customer paid 120.50 for 2 adult tickets and 5 children’s tickets. What is the price of each kind of ticket?

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1 week 2022-01-08T22:55:12+00:00 1 Answer 0 views 0

1. Answer: the price of an adult ticket is \$21.5 while the price of a child ticket is \$15.5

Step-by-step explanation:

Let x represent the price of an adult ticket.

Let y represent the price of a child ticket.

At an amusement park, the cost of 3 adult tickets and 4 children’s tickets is 126.50. This means that

3x + 4y = 126.5 – – – – – – – – – – – 1

Another customer paid 120.50 for 2 adult tickets and 5 children’s tickets. This means that

2x + 5y = 120.5 – – – – – – – – – – 2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 8y = 253

6x + 15y = 361.5

Subtracting, it becomes

– 7y = – 108.5

y = – 108.5/ -7

y = 15.5

Substituting y = 15.5 into equation 1, it becomes

3x + 4 × 15.5 = 126.5

3x + 62 = 126.5

3x = 126.5 – 62 = 64.5

x = 64.5/3 = 21.5