The Jurassic Zoo charges $11 for each adult admission and $7 for each child. The total bill for the 264 people from a school trip was $2140. How many adults and how many children went to the zoo?

59 Adults And 147 Children

Step-by-step explanation:

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.