Write a number in each blank to complete an inequality Lydia can use to find how many pounds of Pumpkin Spice coffee, p, she can buy along with 2 pounds of Dark Roast coffee.

Missing part of the question:

Lydia is at a coffee shop and knows  she can spend no more than $65  before tax. She sees this price list in  the coffee shop.

Item                                               Price per pound

Dark Roast Coffee                       $7.50

Pumpkin Spice Coffee                 $10.50

Step-by-step explanation:

From the question, we understand that she wants to buy 2 pounds of dark roast coffee.

If 1 pound costs $7.50, then 2 pounds cost $15.0 (i.e. $7.50 * 2)

If 1 pound of pumpkin spice coffee costs $10.50, then p pounds cost $10.50p (i.e. $10.50 * p)

So, her total spendings (before tax) is:

Spendings = 15.0 + 10.50p

We also know that she plans to spend not more than $65.

The inequality that represents this scenario is:

Solving further:

Make p the subject

-- approximated

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!