Adult tickets cost $4 and children tickets cost $1. 285 tickets are sold. And $765 is collected. How many adult tickets were sold.?Use substitution or elimination to solve the problem

Expert Answers
pohnpei397 eNotes educator| Certified Educator

The answer to this is that 160 adult tickets were sold.  This means that 125 children's tickets were sold.  Here is how to solve this problem:

Let's call adult tickets A and children's tickets C.

We know that A + C = 285 because that's how many total tickets were sold.

We know that 4A + C = 765.  That's because each adult ticket sold cost $4 so 4 times the number of adult tickets, plus the number of kids tickets ($1 each) make the total amount collected.

Let's use the first equation to find for C.  C = 285 - A.

Now just substitute that into the other equation and you have

4A + 285 - A = 765.

3A = 480

A = 160

bullgatortail eNotes educator| Certified Educator

If adult tickets cost $4, and children's tickets cost $1, and 285 tickets total were sold, and the total amount collected is $765, there can only be one possible answer. I believe you will find that 160 adult tickets were sold (total of $640) and 125 children's tickets were sold (total of $125). Combining these two amounts will give you 285 tickets and a total of $765. Any difference in tickets sold by either adults or children would result in a higher or lower total amount.

neela | Student

In the question the need is to determine the number of adult and child tickets  tickets sold out. So one of the unknown  is x.

We presume  x number of tickets for sdults are sold. The child tickets is automatically must be 285-x.

The collection of revenue from x adult tickets =  number of tickets* rate of tickets = 4x

The collection of revenue from 285-x child tickets = number*rate = (285*x)*1 =285-x.

The total collection  = 4x+285-x algebraically.......(1)

The actual collection = $765..............................(2)

Therefore the required equation of the problem:

Algebraic collection as at (1)  = actual collection as at (2). So,

$(4x+285-x) = %765. Or

4x-x +285 = 765. Or

3x- 765 - 285 = 480. Or

3x = 480. Or

3x/3 = 480/3. So

x = 160  is the number of adult tickets sold.

285 - x = 285 - 160 = 125 is the number of child tickets sold.

Check: 160+125 = 285 and revenue $(160*4+125) =$ (640+125) = $765