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 ∨

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.