Mrs. Delgado purchased notebooks at $2.50 each and pens at $2.00 per package. She spent $19.00 for a total of 8 items. Which system of equations below could be used to find n, the number of notebooks, and p, the number of packages per pens, that Mrs. Delgado purchased?

Step-by-step explanation:

let n be the total number of notebooks.

let p be the total number of pens.

according to the question total number of pen and notebook is 8.

Therefore mathematically

n+p = 8 equation A

cost of one notebook = $2.50

number of notebook = n

therefore total cost of n notebook = n* 2.50 = 2.5n

cost of one pen = $2.00

number of pen = p

therefore total cost of p pen = p* 2.00 = 2p

according to the question total c cost of pen and notebook is $19.00.

Therefore mathematically

2.5n + 2p = 19 equation B

Set of equation as required by question are

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!

900 degrees

step-by-step explanation: