Question

You are buying two kinds of coffee.1 pound of premium coffee costs $3.00.1 pound of regular coffee costs $2.00.You have $15.00 to spend and want to buy 1 pound of premium coffee.Use the number line to draw the solution set that shows all possible numbers of pounds of regular coffee that you could buy. Must be answered as an inequality: greater than, less than, greater than or equal to, less than or equal to, equal to.

Answer 1

Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

`x\leq 7.5\ pounds`

Part 2)
`m+n=(0.76x-0.28)`

Explanation:

Part 1)

Let

x-----> the number of pounds of regular coffee

we know that

The inequality that represent the situation is

`2x\leq 15`

Solve for x

Divide by 2 both sides

`x\leq 15/2`

`x\leq 7.5\ pounds`

The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

The solution of the inequality is the interval ------> (-∞,7.5]

but the number of pounds cannot be a negative number

therefore

The solution is the interval -----> [0,7.5]

see the attached figure

Part 2) we have

`m=0.56x-0.25`

`m=0.20x-0.03`

Adds m and n

`m+n=(0.56x-0.25)+(0.20x-0.03)`

Group terms that contain the same variable

`m+n=(0.56x+0.20x)+(-0.25-0.03)`

Combine like terms

`m+n=(0.76x-0.28)`