Eun-Kyung works as a tutor and earns $60 per hour. She has $792 in savings. She is planning an anniversary party for her parents. She would like to invite 40 guests. The party will cost her $1,520 for food and drinks and $150 for the photographer. She will also have a favor for each of the guests, and each favor will cost $7.50. How many hours must she tutor to have enough money for the party?

the cost of an adult ticket is $21.5

the cost of a child ticket is $15.5

Step-by-step explanation:

Let x represent the cost of an adult ticket.

Let y represent the cost of a child ticket.

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

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

Another customer paid $120.50 for 2 adult tickets and 5 children's tickets. It 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

3x = 64.5

x = 64.5/3

x = 21.5