Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 334 people entered the park, and the admission fees collected totaled 876.00 dollars. How many children and how many adults were admitted? Your answer is number of children equals number of adults equals

Answer 1

By setting up a system of linear equations based on the given admission prices and total collected fees, we find that there were 184 children and 150 adults admitted to the amusement park.

Step-by-step explanation:

The student is dealing with a system of linear equations. We have two unknowns: the number of children and the number of adults who entered an amusement park. The admission fee for children is $1.50, and for adults, it is $4. We know that a total of 334 people entered the park, and the total admission fees collected amounted to $876.00.

Let's denote the number of children as c and the number of adults as a. We can set up the following equations:

c + a = 334 (the total number of people)

1.50c + 4a = 876 (the total amount of money collected)

To solve these equations, we can use either substitution or elimination methods. We will use the elimination method. Multiplying the first equation by 1.50 gives us another equation 1.50c + 1.50a = 501. Now, we subtract this new equation from the second equation in our system to eliminate c:

1.50c + 4a = 876
- (1.50c + 1.50a = 501)

The result is:

2.50a = 375

Dividing both sides by 2.50, we find that:

a = 150

Substituting this value for a into the first equation, we have:

c + 150 = 334

Therefore, c = 334 - 150 = 184.

So, there were 184 children and 150 adults admitted to the amusement park.

Answer 2

Answer: Number of children = 184

Number of adults = 150

Step-by-step explanation:

Let x be the number adults and y be the number of children.

334 people entered the park.

`\Rightarrow\ x+y=334----------(1)`

The admission fee at an amusement park is $1.50 for children and $4 for adults and fees collected totaled 876.00 dollars.

`\Rightarrow\ 1.50x+4y=876----------(2)`

Multiply 4 to equation (1), we get

`4x+4y=1336---------(3)`

Eliminate equation (2) from (3)

`2.50x=460\\\\\Rightarrow\ x=(460)/(2.5)=184`

Put x= 184 in (1)

`184+y=334\\\\\Rightarrow\ y=334-184=150`

∴ Number of children = 184

Number of adults = 150