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

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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) About Me  (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 x%2By=206


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 11x%2B9y=1972


So we have the system:


system%28x%2By=206%2C11x%2B9y=1972%29


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

x%2By=206 Start with the first equation


y=206-x Subtract x from both sides


y=-x%2B206 Rearrange the equation



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

Since y=-x%2B206, we can now replace each y in the second equation with -x%2B206 to solve for x



11x%2B9highlight%28%28-x%2B206%29%29=1972 Plug in y=-x%2B206 into the second equation. In other words, replace each y with -x%2B206. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



11x%2B%289%29%28-1%29x%2B%289%29%28206%29=1972 Distribute 9 to -x%2B206


11x-9x%2B1854=1972 Multiply


2x%2B1854=1972 Combine like terms on the left side


2x=1972-1854Subtract 1854 from both sides


2x=118 Combine like terms on the right side


x=%28118%29%2F%282%29 Divide both sides by 2 to isolate x



x=59 Divide





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


So the first part of our answer is: x=59









Since we know that x=59 we can plug it into the equation y=-x%2B206 (remember we previously solved for y in the first equation).



y=-x%2B206 Start with the equation where y was previously isolated.


y=-%2859%29%2B206 Plug in x=59


y=-59%2B206 Multiply


y=147 Combine like terms



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


So the second part of our answer is: y=147









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

So our answers are:

x=59 and y=147



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