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!

0

Answers ( No )

    0
    2021-11-26T07:11:47+00:00

    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

    0
    2021-11-26T07:12:09+00:00

    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:

    x + y = 870

    If that day is collected 3772.50 dollars, we have:

    3.25x + 6.75y = 3772.50

    So, we have two equations with two unknowns:

    x + y = 870 —–> (1)

    3.25x + 6.75y = 3772.50 —–> (2)

    Clearance of (1):y = 870-x

    Substituting in 2:

    3.25x + 6.75 (870-x) = 3772.50\\3.25x + 6.75 * 870-6.75x = 3772.50\\3.25x-6.75x = 3772.50- (6.75 * 870)\\3.25x-6.75x = 3772.50-5872.5\\-3.5x = -2100

    x = \frac{-2100}{-3.5}\\x = 600

    Thus, there were 600 children at the fair.

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

    y = 870-x\\y = 870-600\\y = 270

    Thus, there were 270 adults at the fair.

    Answer:

    600 children and 270 adults

Leave an answer

Browse
Browse