How many children and how many adults were admitted?

Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 302 people entered the park, and the admission fees collected totaled 828.00 dollars. How many children and how many adults were admitted?

Answer 1

We can set up two equations in two variables and solve the system.

Let A = # adults admitted

Let C = # children admitted

 

1) Since there were 302 people total we know  A+C = 302

2) Children cost $1.50 and adults cost $4 and the total fees were so $828 so

    4A + 1.5C = 828

 

Our equations are:

 

A + C = 302            eqn 1

4A + 1.5C = 828     eqn 2

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We can solve either by substitution or elimination.  I will use substitution

Solve for A in terms of C from eqn 1 and substitute that into eqn 2 to solve for C

 

A = 302-C   from eqn 1

 

4(302-C) + 1.5C = 828

1208 - 4C + 1.5C = 828

-2.5C = 828 - 1208

C = -380/(-2.5) = 152

 

There were 152 children

The number of adults = 302-C = 302-152 = 150

 

Check Answer:  4A + 1.5C = 828

                      4(150) + 1.5(152) = 828

                       600 + 228 = 828

                        828 = 828

The answer checks as valid

Answer 2

This is a system of equations problem.

 

You know that a total of 302 people entered the park. Let x be the number of children and y be the number of adults. Then we get that

x + y = 302

 

We also know that the total admission fee is 828.  Also, we have that it cost children $1.50 while it cost adults $4 to be admitted.  We can then get another equation,

1.50x + 4y = 828

 

now we have to equations and two variable. We need to substitute one of the variables to solve for it.

 

Lets replace y in the second equation.

 

We first figure out the value for y from the first equation.

 

x + y = 302

x - x + y = 302 - x

y = 302 - x

 

Now, we replace y in the second equation.

 

1.50x + 4y = 828

1.50x + 4(302 - x) = 828

1.50x + 1208 - 4x = 828

1208 - 2.5x = 828

1208 - 828 = 2.5x

380 = 2.5x

x = 152

 

We solve for the number of children. Now we can just plug x to either equations and then solve for y which is the number of adults.