The admission fee at a fair is $3.25 for children and $6.75 for adults. on a certain day, 870 people enter the fair and $3,772.50 is collected. write a system of linear equations that you can use to determine how many children and adults attended. be sure to define your variables. solve the system. show your work !

Given that admission fee for 1 child = $3.25

If there are x children then admission fee for x children = $3.25x

Given that admission fee for 1 adult = $6.25

If there are y adults then admission fee for y adults = $6.75y

Then total fee collected = 3.25x+6.75y

Given that On a certain day, 870 people enter the fair then equation will be

x+y=870

or y=870-x...(i)

And  $3,772.50 is collected means we get equation:

3.25x+6.75y = 3772.50

or 325x+675y = 377250...(ii)

Hence required system of equation is {x+y=870, 3.25x+6.75y = 3772.50}

Now we solve both to find values of x and y

Plug (i) into (ii)

325x+675(870-x) = 377250

325x+587250-675x = 377250

587250-350x = 377250

-350x = 377250-587250

-350x = -210000

x=600

now plug value of x into (i)

y=870-x=870-600=270

Hence final answer is:

Number of children = 600

Number of adults = 270

For this case we have the following variables:

x: Represents the number of children at the fair

y: Represents the number of adults at the fair

If 870 people enter the fair we have:

If that day is collected 3772.50 dollars, we have:

So, we have two equations with two unknowns:

-----> (1)

-----> (2)

Clearance of (1):

Substituting in 2:

Thus, there were 600 children at the fair.

To know the number of adults, we cleared and from the equation (1):

Thus, there were 270 adults at the fair.

600 children and 270 adults

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.