How many children and adults entered the fair that day

Question

he admission fee at a fair is $1.50 for children and $4.00 for adults. On a certain day 2200 peoplr enter the fair and $5050 is collected. How many children and adults entered the fair that day

Answer 1

$1.50X + $4.00(2200 - X) =$5050    $1.50X + $8800 - $4.00X = $5050     - $2.50X = - $3750

 

-$2.50X/-$2.50 = -$3750/-$2.50      X = 1500 children      2200 - X = 700 adults 

Answer 2

Hello Camryn,

 

This is an example of solving a system of equations in Algebra 2.

 

The first step is to think about the problem and derive two formulas,

1.) A formula describing the amount of people that enter the fair.

2.) A formula describing the amount of money that was collected that day.

 

The question tells us that children and adults can enter the fair, and that 2200 people entered on a certain day.

We derive the following equation from this: 1.) C + A = 2200. 

This is simply saying that the sum of children and adults entering the fair equals 2200 people.

 

The question tells us that children pay $1.50 and adults pay $4.00. We are also told that $5050 was collected that day.

So, the total of $5050 collected is some ratio of children and adults paying. 

We derive the following equation from this: 2.)  1.5*C + 4*A = 5050

 

We now have 2 equations and 2 unknowns. 

1.) C + A = 2200

2.) 1.5*C + 4*A = 5050

 

You now have to use clever algebra tricks to isolate one variable. You can do that by substitution or by cancellation.

I'll give you a helpful first step: 

If you multiply equation 1.) by (-4), you will get: -4*C - 4*a = -8800.

You can add the modified version of equation 1.) to equation 2.), and the A terms of -4A and 4A will cancel out.

This will leave you solving for C, and completing the rest of the puzzle.

 

Hopefully this helped you,

Joseph 

Answer 3

Let c be the number of children and let a be the number of adults.

 

So first of all we know that a + c = 2200

 

How much was collected for children?  That's 1.50 c, since it costs $1.50 for each child.

 

Similarly 4a was collected for children.

 

Since a total of $5050 was collected, you can write another equation:

 

1.5c + 4a = 5050

 

Now we just have to solve the two equations together.

 

From the first equation we know that a = 2200 - c.

 

So substitute that into the second equation.

 

1.5c + 4 (2200 - c) = 5050

1.5c + 8800 - 4c = 5050

-2.5c + 8800 = 5050

-2.5c = 5050 - 8800

-2.5c = -3750

c = 1500

 

So there were 1500 children.

 

Since there were a total of 2200 people, there were 700 adults.