The admission fee at an amusement park is $1.75 for children and $5.60 for adults.

Question

The admission fee at an amusement park is $1.75 for children and $5.60 for adults. On a certain day, 340 people entered the park, and the admission fees collected totaled 1288 dollars. How many children and how many adults were admitted?

number of children equals:
number of adults equals:

Answer 1

Hi Treena!

First, we need to write an equation using variables for the number of adults and the number of children, and the total admission fees.  

I personally would pick A=the number of adults, C=the number of children, and T=total $ so that they're easy to remember.

Then we write that equation:

T=5.60A+1.75C

because the total cost will be $5.60 times the number of adults plus $1.75 times the number of children. 

We can then substitute T= 1288

1288= 5.60A + 1.75C

Because there are two variables in this equation, we need to set up another equation:

A(number of adults) +C(number of children) = P(total number of people)

We can then substitute P=340:

A+C=340

We now have a system of equations:

1288= 5.60A +1.75C

A+C=340

There are a number of ways to solve systems of equations:

We can use substitution, which would probably be the easiest in this case of we can choose:

So now we solve for either A or C using the second equation:

A= 340-C or C= 340-A

We'll proceed for now with A=340-C

Then, substitute this for A in the first equation:

1288= 5.60(340-C) +1.75C

Now we only have one variable in our equation, so it will be easy!

First, multiply (340-C) by 5.60:

1288=(5.60*340) - (5.60*C) + 1.75C

1288= 1904 - 5.60C +1.75C

Then combine like terms:

1288= 1904 -3.85C

Subtract 1904 from both sides:

1288-1904= -3.85C

-616= -3.85C

Divide both sides by -3.85:

-616/-3.85=C

C=160

Now we have the answer for C that we just plug back into the A+C=340 equation:

A+ 160=340

A=340-160

A= 180

Now plug your answers back into the original equation to check:

1288= 5.60A +1.75C

1288=? 5.60(180) + 1.75(160)

1008+ 280=?1288

Yes our answers checked out!

Hope this helps :)

Answer 2

Let x = number of children. Therefore, the number of adults is 340 - x.

We can the calculate the number of children by multiplying the number of each type of ticket times the price:

1.75x + 5.60(340 - x) = 1288

Simplify to solve for x, and that will give you the number of children admitted. Then subtract it from 340 to determine the number of adults.