SOLUTION: Problem: The Jurassic Zoo charges $28.00 for each adult admission and $12.00 for each child. The total bill for 454 people from a school trip was $3860.00. How many adults and how

Question 199611: Problem: The Jurassic Zoo charges $28.00 for each adult admission and $12.00 for each child. The total bill for 454 people from a school trip was $3860.00. How many adults and how many children went to the zoo? how would set this problem up useing polynomials
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
let adults be given by x
let children be given by y

Now solve this set of equations to see if there is an 'reasonable' answer
As you can, the answer ends up being a negative number of adults. So the numbers given in the problem aren't 'correct'

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition

Lets start with the given system of linear equations

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 1 and 28 to some equal number, we could try to get them to the LCM.

Since the LCM of 1 and 28 is 28, we need to multiply both sides of the top equation by 28 and multiply both sides of the bottom equation by -1 like this:

Multiply the top equation (both sides) by 28
Multiply the bottom equation (both sides) by -1

So after multiplying we get this:

Notice how 28 and -28 add to zero (ie )

Now add the equations together. In order to add 2 equations, group like terms and combine them

Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.

So after adding and canceling out the x terms we're left with:

Divide both sides by to solve for y

Reduce

Now plug this answer into the top equation to solve for x

Plug in

Multiply

Reduce

Subtract from both sides

Make 454 into a fraction with a denominator of 4

Combine the terms on the right side

Multiply both sides by . This will cancel out on the left side.

Multiply the terms on the right side

So our answer is

,

which also looks like

(, )

Notice if we graph the equations (if you need help with graphing, check out this solver)

we get

graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).

and we can see that the two equations intersect at (,). This verifies our answer.

RELATED QUESTIONS
how would set this problem up useing polynomials:The Jurassic Zoo charges $28.00 for each (answered by jim_thompson5910)

The Jurassic zoo charges $9 for each adult admission and $5 for each child. The total... (answered by TimothyLamb)

The Jurassic zoo charges $14 for each adult admission and $8 for each child. The total... (answered by josgarithmetic)

The Jurassic Zoo charges $6 for each adult admission and $4 for each child. The total... (answered by josmiceli)

The Jurassic Zoo charges $28.00 for each adult admission and $12.00 for each child. The... (answered by jim_thompson5910)

The Jurassic zoo charges $13 for each adult admission and $8 for each child. The total... (answered by josgarithmetic)

The Jurassic zoo charges $6 for each adult admission and $4 for each child. The total... (answered by josgarithmetic)

The Jurassic Zoo charges $11 for adult admission and $9 for each child. the total bill... (answered by jim_thompson5910)

The Jurassic Zoo charges $12 for each adult admission and $7 for each child. The... (answered by josgarithmetic,greenestamps)