Question

Sarah is planning to spend a week at her friend’s summer house in Miami Beach. All meals will be provided by her friend’s parents, but Sarah still needs at least $500 to pay for her airfare and personal expenses for the week. She is selling bracelets and earrings to fund her trip. A graph representing this situation is shown below.

Questions:
1.This region represents the combinations of bracelets and earrings that Sarah must sell in order to get a minimum of $500 profit to pay for her trip.
2.This region represents the area where Sarah sells a lot of earrings but not enough bracelets to reach her $500 goal.
3.This region represents the area where Sarah sells a lot of earrings but not enough bracelets to reach her $500 goal.

graph below ∨↓↓↓↓

Answer 1

the first one is region 2 and the second is region 3 i think

Answer 2

Given:
x > 50
2x + 3y > 500

Bracelet is represented by x.
Earrings is represented by y.

Since x > 50 let us assume that x = 50 to get the value of y in the inequality equation.

2x + 3y > 500
2(50) + 3y > 500
100 + 3y > 500
-100 -100
3y > 400
÷3 ÷3
y > 133 1/3

x > 50 ; y > 133 1/3

Let us assume that no bracelet was sold. x = 0 ; y =?

2x + 3y > 500
2(0) + 3y > 500
0 + 3y > 500
÷ 3 ÷3
y > 166 2/3

Let us assume that no earrings was sold; y = 0 ; x = ?
2x + 3y > 500
2x + 3(0) > 500
2x + 0 > 500
2x > 500
÷2 ÷2
x > 250

Let us assume that we sold have of each item.
x = 250/2 = 125 ; y = 166 2/3 ÷ 2 = 100

2x + 3y > 500
2(125) + 3(100) > 500
250 + 300 > 500
550 > 500

To get at least $500, Sarah needs to sell at least 100 bracelets and 100 earrings.