Question

The admission fee at an amusement park is $2.50 for children and $5.40 for adults. On a certain day, 324 people entered the park, and the admission fees collected totaled $1390. How many children and how many adults were admitted?
number of children equals

number of adults equals

Answer 1

Answer:

• 124 children
• 200 adults

Step-by-step explanation:

It usually works well to let a variable represent quantity of the highest-value contributor. Here, that is the quantity of adult tickets.

Let "a" represent the number of adult tickets sold. Then (324-a) is the number of admission fees for children. The total revenue is ...

  5.40a +2.50(324 -a) = 1390

  2.90a +810 = 1390 . . . . eliminate parentheses

  2.90a = 580 . . . . . . . . . subtract 810

  a = 200 . . . . . . . . . . . . . .divide by 2.90

The number of children admitted was 124; the number of adults admitted was 200.

Answer 2

Answer: number of children equals 124

number of adults equals 200

Step-by-step explanation:

Let x represent the number of children that were admitted.

Let y represent the number of adults that were admitted.

On a certain day, 324 people entered the park. It means that

x + y = 324- - - - - - - - - - - 1

The admission fee at an amusement park is $2.50 for children and $5.40 for adults. The admission fees collected totaled $1390. It means that

2.5x + 5.4y = 1390- - - - - - - - - -1

Substituting x = 324 - y into equation 1, it becomes

2.5(324 - y) + 5.4y = 1390

810 - 2.5y + 5.4y = 1390

- 2.5y + 5.4y = 1390 - 810

2.9x = 580

x = 580/2.9

x = 200

x = 324 - y = 324 - 200

x = 124