Question

I WILL GIVE BRAINLIEST AND POINTS! Plz help me with this question. Help with part C plz

Sarah has $8 and wants to buy a combination of cupcakes and fudge to feed at least four siblings. Each cupcake costs $2, and each piece of fudge costs $1.

This system of inequalities models the scenario:

2x + y ≤ 8
x + y ≥ 4

Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)

Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (3 points)

Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

Answer 1

Answer:

First solve the two inequalities by putting them in function format:

$2x + y \leq 8\\y\leq -2x+8$      $x + y\geq 4\\y\geq -x+4$

Part A:

For the inequality $2x+y\leq 8$ , the solution set would be the area under the graphed line of $y=-2x+8$, where the y-values are smaller, since it asks for y is smaller than or equal to $-2x+8$. Because it is a $\leq$, the line would be filled, not dotted, and the points on the line would also be included in the solution.

For the inequality $x+y\geq 4$, the solution set would be the area above the graphed line of $y=-x+4$, where the y-values are larger, since it asks for y is larger than or equal to $-x+4$. Because it is a $\geq$, the line would be filled, not dotted, and the points on the line would also be included in the solution.

The solution set that met both inequalities would be the area on the graph that covers the solution for both inequalities. The y-values has to be smaller than or equal to $-2x+8$, but greater than or equal to $-x+4$, meaning they lie within the range of $4-x\leq y\leq 8-2x$. It would be the area double-shaded on the graph.

Part B:

Substitute in the point (8, 10) into both inequalities and see if it's true:

$y\leq -2x+8\\10\leq -2(8)+8\\10\leq 8-16\\10\leq -8$       $y\geq -x+4\\10\geq -(8)+4\\10\geq 4-8\\10\geq -4$

Even though it's true in the inequality $y\geq -x+4$, it's false in the inequality $y\leq -2x+8$ because 10 is not smaller than -8. Therefore the point (8, 10) is not included in the solution area for the system.

Part C:

A point within the solution would be the intersection point of $y=-2x+8$ and $y=-x+4$. Therefore, set those two functions equal to each other to find the coordinates of intersection:

$-2x+8=-x+4\\x-2x=4-8\\-x=-4\\x=4$        $y=-x+4\\y=-(4)+4\\y=4-4\\y=0$        $y=-2x+8\\y=-2(4)+8\\y=8-8\\y=0$

The intersection point and a solution to the system of inequality would be (4, 0). This means Sarah can buy 4 cupcakes and 0 fudge, while meeting her budget of $8 and being able to feed at least four siblings.

Answer 2

The given inequality gives the possible combination of the variables that

meet the set criteria.

• Part A: Please find attached the graphs of the inequalities.

• Part B: the point (8, 10) is not included in the solution set.

• Part C: At point (0, 8) Sara buys only 8 fudges for $8.

Reasons:

Part A: The graph consists of two solid lines of negative slope, with the

lower region of the graph having the steeper slope being shaded while the

area above the other line is shaded.

The solution set is in a triangle with vertices (0, 8), (0, 4), and (4, 0)

Part B: Based on the above solution set described above, we have that the point (8, 10) is not included in the solution set.

Part C: A point in the solution set is (0, 8)

The above point means that Sarah can buy 8 pieces of fudge and 0

cupcakes for $8.

Learn more about graphs of an inequality here:

https://brainly.com/question/17136458