Question

Trenton is going to the store to buy candy. Bags of candy corn cost $3 and bags of chocolate cost $5. He needs to buy at least 20 bags of candy and he cannot spend more than $60. 1. Define your variables 2. Write a system of linear inequalities to model the situation.3. Solve the system of inequalities by any method of your choice4. Explain/show work for the method you chose

Answer 1

C = Candy corn

$3

Ch = Chocolate

$5

20 bags of candy at least

Cannot spend more than $60

1. Define your variables

x = Candy corn

y = Chocolate

2. Wirte a system of linear inequatlities

20 bags of candy at least

`x+y\ge20`

Cannot spend more than $60

`3x+5y\le60`

3. Solve the system of inequalities

Blue = 3x+5y < 60

Pink = x+y > 20

Now,

Let's find the point where the two lines intersect

`\begin{gathered} 3x+5y=60 \\ x+y=20 \\ \\ \end{gathered}`
`\begin{gathered} 3x+5y=60 \\ + \\ -5(x+y=20) \\ \\ 3x+5y=60 \\ + \\ -5x-5y=-100 \\ \\ 3x-5x+5y-5y=60-100 \\ -2x+0=-40 \\ 2x=40 \\ x=20 \end{gathered}`

Now for y

`\begin{gathered} x+y=20 \\ y=20-x \\ y=20-20 \\ y=0 \end{gathered}`

x = 20 Candy corn

y = 0 chocolate

You need to buy 20 Candy corn and spend $ 60

4. Explain/show work

a. Finding the intersection by trading inequalities for equality

b. Use the elimination method to find the solution

c. See if the solution meets the inequality