Answer:
Let's define the variables:
x = number of Cherrie pounds you buy
y = number of Grape pounds you buy.
The total cost of buying that will be:
x*$4 + y*$2.50
And this must be no more than $15, then we have the inequality:
x*$4 + y*$2.50 ≤ $15
And we also know that you need at least 5 pounds in total, then we will have:
x + y ≥ 5
We have the set of inequalities:
x + y ≥ 5
x*$4 + y*$2.50 ≤ $15
To graph them, a easy way is to write them as lines, and just graph the lines:
y ≥ 5 - x
y ≤ ($15 - x*$4)/$2.50
in the first inequality, we have the symbol ≥, this means that we will have a solid line and we must shade above the line.
In the second inequality, we have the symbol ≤, this means that we will have a solid line and we must shade below the line.
And we also must include the conditions:
x ≥ 0
y ≥ 0
Because you can only buy positive numbers of fruit.
This will restrict us to the first quadrant only
Then the graph will be the one shown below.
Where the solutions are the ones in the double shaded region in the first quadrant.
The inequalities that represent the given data are [tex]\rm y \leq \dfrac{15-4x}{2.5}[/tex] and [tex]\rm y\geq 5-x[/tex] and the graph of these inequalities is attached below.
Given :
The following steps can be used in order to determine the graph showing the amount of each fruit you can buy:
Step 1 - Let 'x' be the total amount of cherries in pounds and let 'y' be the total amount of grapes in pounds.
Step 2 - The inequality that represents the total amount of fruits you can buy is given below:
[tex]\rm 4x+2.5y\leq 15[/tex]
[tex]\rm y \leq \dfrac{15-4x}{2.5}[/tex]
Step 3 - The inequality that represents the total amount of fruits you need to buy:
[tex]\rm x+y\geq 5[/tex]
[tex]\rm y\geq 5-x[/tex]
Step 4 - The graph that represents the inequalities evaluated in the above steps is attached below.
For more information, refer to the link given below:
https://brainly.com/question/19491153
