Answer:
The adult tickets are <u>400</u> and the children tickets are <u>300</u>.
Step-by-step explanation:
Given:
At a carnival, 700 tickets were sold for a total amount of $5500. An adult ticket cost $10
and a children's ticket cost $5.
Now, to find the number of adult tickets and the number of children's tickets sold.
<em>Let the number of adult tickets be </em>
<em />
<em>And let the number of children tickets be </em>
<em />
So, the total number of tickets sold:
![x+y=700\\\\y=700-x\ \ \ ....(1)](https://tex.z-dn.net/?f=x%2By%3D700%5C%5C%5C%5Cy%3D700-x%5C%20%5C%20%5C%20....%281%29)
Now, the total amount of tickets:
![x(10)+y(5)=5500](https://tex.z-dn.net/?f=x%2810%29%2By%285%29%3D5500)
Substituting the value of
from equation (1):
![x(10)+(700-x)(5)=5500\\\\10x+3500-5x=5500\\\\5x+3500=5500](https://tex.z-dn.net/?f=x%2810%29%2B%28700-x%29%285%29%3D5500%5C%5C%5C%5C10x%2B3500-5x%3D5500%5C%5C%5C%5C5x%2B3500%3D5500)
<em>Subtracting both sides by 3500 we get:</em>
<em />
<em />
<em>Dividing boths sides by 5 we get:</em>
<u />
<u>The number of adult tickets = 400.</u>
Now, substituting the value of
in equation (1) we get:
![y=700-x\\\\y=700-400\\\\y=300.](https://tex.z-dn.net/?f=y%3D700-x%5C%5C%5C%5Cy%3D700-400%5C%5C%5C%5Cy%3D300.)
<u>The number of children tickets = 300.</u>
Therefore, the adult tickets are 400 and the children tickets are 300.