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Sarah is selling bracelets and earrings to make money for summer vacation.

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Anonymous
0

The bracelets cost $2 and the earrings cost $3. She needs to make atleast 500.

Write an inequality to represent the income from the jewelry sold.


  • Sarah knows that she will see more than 50 bracelets. Write an inequality to represent this situation
  • Graph the two inequalities and shade the intersection
  • Identify a solution. How many bracelets and earings can Sarah sell?


Sangeetha Pulapaka
1

1.

Let x = no. of bracelets sold or made

Let y = no. of earrings sold or made

Since the price of the number of bracelets is $2, the price of the number of earrings is $3 we write

2 x + 3 y \geq 50

Since Sarah knows she will sell more than 50 bracelets we write x\gt 50

This is our second inequality


2.

Graphing the two inequalities we get the below graph.



3.Our inequality is 2x+3y \geq 500

(100,100) is a solution to the inequality since plugging in x = 100 and y = 100 we get 500= 500. Sarah can sell 100 bracelets and 100 earrings to make at least $500.

(200,100) is also a solution to the inequality, since plugging in x = 200 and y = 100 we get 400 + 300 = 700 \gt 500. So, Sarah can also sell 200 bracelets and 100 earrings to make at least $500.

(200,200) is also a solution to the inequality since plugging in x = 200 and y = 200 we get 400 + 600 =1000 \gt 500. This means that, Sarah can also sell 200 bracelets and 200 earrings to make at least $500.



Skills you may want to recall:

What is an inequality

https://www.mathsisfun.com/definitions/inequality.html

How to graph an inequality

https://www.mathsisfun.com/algebra/graphing-linear-inequalities.html