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)

Given : 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.

To Find : Form System of inequalities

Solution:

number of  cupcakes  = x

number of  fudge  = y

2x + y  ≤ 8

x + y ≥ 4

Solution of the system lies with in the triangle formed by points

(0 , 4) , ( 0 , 8)  , (  4, 0)

point (8, 10) is not included in the solution area for the system

as 2(8) + 10  = 26 >  8

(0 , 4)

She will buy  4 fudges only for 4 siblings in Rs 4

(  4, 0)

She will buy  4 cupcakes only for 4 siblings in Rs 8

( 0 , 8)

She will buy  8 fudges only for 4 siblings ( 2 for each )  in Rs 8

If she has to buy  maximum then ( 0 , 8) is best suited

if she has to spend minimum then ( 0 , 4) is best suited

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