Question

five hundred tickets were sold for a saturday evening performance of a play. the tickets cost 7.50 for adults and 4.00 for children. A total of 3312.50 was received for all of the tickets sold that saturday. How many adults attends the play?

Answer 1

Answer:

There are 375 Adults in the group.

Step-by-step explanation:

- We know that 500 Tickets were sold. This means there were 500 people who attended the Evening Performance.

- The Tickets Cost 7.50$ For Adults

& 4$ for Children.

- And we also know that the number of $ is 3312.50

So how many adults attend the Play?

- Let's Set a for Adult

- Let's Set c for Children

a + c = 500

a = 500-c

Now let's replace it in our equation...

7.50a + 4c = 3312.50

7.50(500-c) + 4c = 3312.50

3750 - 7.5c + 4c = 3312.50

3750-3312.50 = 7.5c - 4c

437.5 = 3.5c

437.5/3.5 = c  

125 = c

Now we know that there were 125 children.

Now let's subtract it from the total number of people.

500-125 = 375

Meaning that there are 375 Adults in the group.

Answer 2

x + y = 500
7.50x + 4y = 3312.50.....
such that
We then multiply the top equation by -4 to find the number of adults first
-4×-4y=-2000
7.50x + 4y = 3312.50
3.5x = 1312.5,
x= 375 Adults attended
..Then divide 3.5 such that
Then we plug this into the first equation such that
375 + y = 500......
•Then subtract 375 such that
y= 125 children attended

I hope this helped!