Tickets are $4.25 for children $9.75 for adults and $5.50 for senior citizens. Total revenue from tickets sold was $8037.50. How many children adult and senior citizen tickets were sold?

Answer 1

We have 3 unknown quantities but only one equation.

C is the number of children's tix

A is the number of adult tix

S is the number of senior citizen tix

4.25C + 9.75A + 5.5S = 8037.50 <--- this is the first and only equation

Typically the total # of tickets is given.

Suppose there are N tickets sold altogether per the receipts.

Then

C + A + S = N <--- this is the 2nd equation

(It would really be nice if you can tell us what

the total number of tickets, or N, really is!!!)

Since there is no 3rd equation due to lack of data, there is

a free variable, or 1 degree of freedom. Once selected, one

of the other variables can be eliminated, and they are written

in terms of the free variable.

Without loss of generality, let A be free the variable.

Once chosen, the system becomes:

4.25C + 5.5S = 8037.5 - 9.75A

C + S = N - A <--- please label this equation ALPHA;

we will need it later!

Now it is a 2 x 2 system of equations which can easily be solved

by substitution.

C+S = N - A ---> C = N - A - S

4.25 ( N - A - S ) + 5.5 S = 8037.5 - 9.75A <--- substitutes into the first equation

4.25N - 4.25A - 4.25S + 5.5S = 8037.5 - 9.75A <--- distributive

4.25N - 4.25A + 1.25S = 8037.5 - 9.75A <-- combines like terms (CLT) containing S on left side

1.25S = 8037.5 - 9.75A - 4.25N + 4.25A <-- moves the fixed constant N and the free var A

to right side

1.25S = 8037.5 - 5.5A - 4.25N <--- combines like terms again (CLT) on right side

S = (8037.5 - 5.5A - 4.25N)/ 1.25

Keep in mind that A,S, and C represent the number of tickets

and should be positive integers, so you must be careful

what values you pick for A and N

For example, suppose there were N=1000 tickets sold altogether

and A=675 adult tickets sold.

Then S = (8037.5 - 5.5*675 - 4.25*1000)/1.25 = 60

and

A + S + C = 1000

675 + 60 + C = 1000

735 + C = 1000

C = 265

Finally 675 * 9.75 + 4.25 * 265 + 5.5 * 60 = 8037.5

This is what happens when some of the given information

is not posted. It makes thing VERY complicated

Please repost.