The admission fee at an amusement park is $6.50 for children and $15.00 for adults. On a certain day, 337 people entered the park, and the admission fees collected totaled $3,423.00. How many children and how many adults were admitted?

192 children and 145 adults were admitted.

Step-by-step explanation:

Let c represent the amount of children and let a represent the amount of adults.

Total fees for children = (Fee for one child) x (Amount of children) = 6.5c

Total fees for adults = (Fee for one adult) x (Amount of adults) = 15a

Total fees = Total fees for children + Total fees for adults

3423 = 6.5c +15a

We know that the amount of people who entered the park was 337. Therefore a+c=337, which means a=337-c.

Sub this in to the equation above to get:

3423 = 6.5c +15 (337-c)

3423 = 6.5c + 5055 - 15c

-1632 = -8.5c

c = 192

So there were 192 children.

Since a=337-c and c=192, a=337-192=145. So there were 145 adults.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

a

step-by-step explanation: