Question
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Model with Mathematics Felicia spends \( \$ 50 \) on materials to make welry, and she plans on selling the pieces for \( \$ 7 \) each. A friend donates to get her started. Write an inequality to find the number of pieces of welry Felicia can sell and make a profit.

Ask by Rodriguez Marsh. in the United States
Feb 26,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Felicia needs to sell at least 8 pieces of jewelry to make a profit.

Solution

Let x represent the number of pieces of jewelry sold. Felicia's revenue from selling x pieces is 7x dollars, and her total cost is $50. To make a profit (i.e., revenue > cost), the inequality is:   7x - 50 > 0 Simplify the inequality:   7x > 50 Divide both sides by 7:   x > 50/7 Since 50/7 is approximately 7.14, Felicia must sell at least 8 pieces to make a profit.

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Extra Insights

To make a profit, Felicia's earnings from selling the jewelry must exceed her initial investment of \( \$ 50 \). If we let \( x \) represent the number of pieces of jewelry she sells, the situation can be modeled with the inequality \( 7x > 50 \). Solving this gives her the minimum number of pieces she needs to sell to start making a profit. As Felicia dives into her jewelry-making venture, it’s important for her to keep track of her costs and earnings. She should maintain clear records of materials used and sales made. This way, she can not only determine her profit but also refine her pricing strategy and consider future expenses, leading to savvy business decisions and that glimmering success she aims for!

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