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 certian 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?

a.
100 adults
c.
200 adults
b.
150 adults
d.
250 adults

Answer 1

After setting up a system of equations based on the given prices for tickets and the total revenue, we can solve to find that 250 adults attended the zoo.

Step-by-step explanation:

The zoo tickets problem is a system of linear equations problem, where we have to find out the number of adults who visited the zoo based on the given cost for children, teenagers, and adults, and the ratio provided for teenagers to children.

Let's define three variables where c is the number of children, t is the number of teenagers, and a is the number of adults. We can set up the equations based on the cost of tickets and the total revenue:

4c + 5t + 6a = $5300 (Total revenue equation)

c + t + a = 1200 (Total number of visitors)

(t/c) = 3/8 (For every 3 teenagers, 8 children went to the zoo)

To solve for a, we can rearrange the equations and use substitution or elimination methods. After solving, we find that the number of adults who went to the zoo is 250.

Answer 2

c/t=8/3, c=8t/3

a+c+t=1200, using c from above:

a+8t/3 +t =1200

3a+8t+3t=3600

11t+3a=3600

t=(3600-3a)/11 and from earlier we said c=8t/3, and using this with t we just found:

c=(28800-24a)/33

5300=6a+5t+4c, using c and t from earlier

5300=6a+(18000-15a)/11+(115200-96a)/33 make the common denominator 33...

174900=198a+54000-45a+115200-96a

57a=5700

a=100

So 100 adult tickets were sold.