Search 75,707 tutors
FIND TUTORS
Ask a question
0 0

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

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:

Tutors, please sign in to answer this question.

2 Answers

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 :)

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.

Comments

The admission fee at an amusement park is $3.75 for children and $6.40 for adults. On a certain day, 295 people entered the park, and the admission fees collected totaled 1464 dollars. How many children and how many adults were admitted?

number of children equals
number of adults equals

Comment