Question

The admission fee at an amusement park is $3.50 for children and $7.00 for adults. On a certain day, 331 people entered the park, and the admission fees collected totaled $1,771.00 dollars. How many children and how many adults were admitted?

Answer 1

Answer:

156 children

175 adults

Step-by-step explanation:

Let's call x the number of children admitted and call z the number of adults admitted.

Then we know that:

$x + z = 331$

We also know that:

$3.50x + 7z = 1,771.00$

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -7 and add it to the second equation:

$-7x - 7z = -2,317$

$3.50x + 7z = 1,771$

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$-3.5x = -546$

$x =\frac{-546}{-3.5}\\\\x=156$

Now we substitute the value of x in the first equation and solve for the variable z

$156 + z = 331$

$z = 331-156$

$z = 175$

Answer 2

Let c be children and a adults.

3.5c + 7a = 1771 (the total revenue is equal to the amounts made off of people)

c + a = 331 (total number of people)

The second formula becomes a = 331 - c. This can be substituted into the first formula.

3.5c + 7(331 - c) = 1771 = 7*331 - 3.5c = 1771. 7*331 = 2317, so 3.5c = 2317 - 1771 = 546.

546/3.5 = 156 = c (number of children).

c + a = 156 + a = 331 => a = 331 - 156 = 175 (number of adults).

There are 156 children and 175 adults