## 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 collec Question 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 PLEASE!

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1. 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

Number of children = 600

2. 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.