550 people use a public swimming pool the prices are 1.75$ for children and 2.25$ for adults the receipts for admission totaled is 1153.00$ How many children were at the pool

There were 169 children at the pool.

Step-by-step explanation:

Given:

Total number of people = 550

Price per child = $1.75

Price per adult = $2.25

Total cost of the admission receipts = $1153.00

Let the number of children be 'x' and number of adults be 'y'.

As per question:

Total number of people is equal to total children and total adults. So,

Total cost of admission is equal to the sum of cost of total children and total adults. So,

Multiplying equation (1) by 1.75 and subtracting the result equation from equation (2). This gives,  

So, there were 381 adults at the pool. Now, the number of children is equal to:

Therefore, there were 169 children at the pool.

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: