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?

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

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,