Need help please.

Question

tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. in the high season, 1200 people come to the zoo every day. on a certain day, the total revenue at the zoo was $5300. for every 3 teenagers, 8 children went to the zoo. how many adults went to the zoo?

Answer 1

You have three variables: Let `C` be the number of children, `T` the number of teenagers, and `A` the number of adults. You're told that 1200 people go to the zoo every day. In math terms, that `C + T + A = 1200`.

You're also told that total revenue was $5300. The total revenue from children is `$4 * C`, from teenagers is `$5 * T`, and from adults is `$6 * A`. All together, you have `4C + 5T + 6A = 5300`.

Finally, you're told that for every three teenagers (T/3), there are eight children (C/8). That is `T/3 = C/8`.

So we have three unknowns, C, T, A. And we have three equations

C + T + A = 1200

4C + 5T + 6A = 5300

8T = 3C

Answer 2

This is a "messy" problem!!!! I will not solve it for you, but I will tell you how to do it.

Let C=# of children, T=# of teens, A=#adults

The total # attending = 1200 = C + T + A

The income = 5300 + 4C + 5T + 6A

and 8T = 3C comes from the 8:3 ratio of kids to teens.

Use this ratio equation to get an expression for C or T, e.g C = 8T/3

Now substitute this into the first 2 equations. This will give you 2 linear equations in T and A.

This is where the mess comes in: you will have to clear fractions and collect terms CAREFULLY!.

Then solve the linear set. There will likely be no easy method. If you know how to do determinants, this will be the most direct way to get A. Otherwise, just slug your way ... probably eliminate T if you can to get the answer for A.