Question

museum had a total of 224 visitors on Tuesday. Visitors older than 18 years paid $12 and visitors 18 years or younger paid $8 x+y=224 , 12x+8y=2520. How many visitors were 18 or younger ?

Answer 1

Answer

The visitors that were 18 years or younger = 42.

Explanation

Given that:

The total number of visitors on Tuesday = 224

The visitors older than 18 years paid $12

The visitors 18 years or younger paid $8

Representing visitors older than 18 years as x and visitors 18 years or younger paid $8 as y, the system of equations below were generated:

x + y = 224 , 12x + 8y = 2520

What to find:

The visitors that were 18 years or younger.

Step-by-step solution:

To get the visitors that were 18 years or younger, solve for y in the system of equation using the elimination method.

$\begin{gathered} x+y=224----i\times12 \\ \\ 12x+8y=2520---ii \\ \\ Multiply\text{ }(i)\text{ }by\text{ }12 \\ \\ 12x+12y=2688----iii \\ \\ 12x+8y=2520---ii \\ \\ Now\text{ }substract\text{ }(ii)\text{ }from\text{ }(iii) \\ \\ 4y=168 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }4 \\ \\ \frac{4y}{4}=\frac{168}{4} \\ \\ y=42 \end{gathered}$

Therefore, the visitors that were 18 years or younger are 42.

To get visitors older than 18 years, that is to solve for x, substitute y as 42 into (i):

$\begin{gathered} x+y=224-----i \\ \\ x+42=224 \\ \\ x=224-42 \\ \\ x=182 \end{gathered}$

Hence, the number of visitors older than 18 years is 182.