Aswimming pool charges $6 for adults and $4 for children. on a particular day, they made $1,326 in admissions. if a total of 289 people paid to swim, how many kids and how many adults

Children:  204

Adults:  85

Step-by-step explanation:

Representation:  let k represent the number of children and a the number of adults.  

Equations:  k + a = 289 (numbers of people)

                   ($4/child)k + ($6/adult)a = $1,326

Let's solve this system of equations by substitution. Since k + a = 289, a = 289 - k.  Substituting 289 - k for a above, we get this equation in one variable:

($4/child)k + ($6/adult)(289 - k), or, without units, 4k + 1734 - 6k = 1326.

The next step is to combine like terms:  -2k = -408.

Dividing both sides by -2, we get k = 204.  There are 204 children in the pool and 289 - 204 adults, or 85 adults.

Children:  204

Adults:  85

a. she will receive a refund of $278.

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!