Question

the art museum had a total of 224 visitors on Tuesday. Visitors older than 18 paid 12 dollars for admission. Visitors 18 or younger paid 8 dollars for admission. The museum collected a total of 2,520 dollars. How many visitors were 18 or younger?

Answer 1

The number of visitor 18 years or younger than 18 years is 42 .

Explanation:

Given as :

The total number visitor in the museum = 224

The price of admission for visitor older than 18 years = $ 12

The price of admission for visitor 18 years or younger than 18 years = $ 8

The total price of tickets = $ 2,520

Let The number of visitor older than 18 years = x

And The number of visitor 18 years or younger than 18 years = y

Now, According to question

The total number visitor in the museum = 224

Or, The number of visitor older than 18 years + The number of visitor 18 years or younger than 18 years = 224

Or, x + y = 224

And $ 12 x + $ 8 y = $ 2,520 ..........A

Or, $ 12 × ( x + y ) = $ 12 × 224

Or, $ 12 x + $ 12 y = $ 2688 ..........B

Solving Eq A and B

Or, ( $ 12 x + $ 12 y ) - ( $ 12 x + $ 8 y ) = $ 2688 - $ 2520

Or, ( $ 12 x - $ 12 x ) + ( $ 12 y - $ 8 y ) = $ 168

Or, 0 + 4 y = 168

∴ y =
`(168)/(4)`

I.e y = 42

So, The number of visitor 18 years or younger than 18 years = y = 42

And ∵ x + y = 224

I,e x = 224 - y

or, x = 224 - 42

∴ x = 182

So, The number of visitor older than 18 years = x = 182

Hence The number of visitor 18 years or younger than 18 years is 42 . Answer