Question

There are 150 adults and 225 children at a zoo. If the zoo makes a total of $5100 from the

entrance fees, and the cost of an adult and a child to attend is $31 dollars, how much does it cost each
for a parent and a child?

Answer 1

It costs $25 for a parent and $6 for a child

Explanation:

Let x be the cost it takes for an adult to enter, and y be the cost it takes for a child to enter then...

x+y=31

150x+225y=5100

We can write the first equation in terms of x by subtracting y from both sides...

x=31-y

Now, we can solve the system of equations by substitution (substitute 31-y for x)...

150(31-y)+225y=5100

Distribute the 150 to the terms inside of the parentheses

150(31)-150(y)+225y=5100

4650-150y+225y=5100

Combine like terms

4650+75y=5100

Subtract 4650 from both sides

75y=450

Divide both sides by 75

y=6

Plug 6 back in for y to solve for x:

x=31-y=31-6=25

It costs $25 for a parent and $6 for a child