SOLUTION: The Jurassic Zoo charges $11 for adult admission and $9 for each child. the total bill for the 206 people from a school trip was $1972. how many adults and how many children went

Question 189604: The Jurassic Zoo charges $11 for adult admission and $9 for each child. the total bill for the 206 people from a school trip was $1972. how many adults and how many children went to the zoo?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of adults and y=# of children

Since there were a total of 206 people, this means that

Also, because "The Jurassic Zoo charges $11 for adult admission and $9 for each child. the total bill for the 206 people from a school trip was $1972", this means that

So we have the system:

Let's solve it by substitution

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 1854 from both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

This means that 59 adults and 147 children went to the zoo.

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