Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A (first text box) Write and solve an inequality to show how many pendants Kelsey should make. Show the steps of your solutions. Part B (second text box) Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit? Answer in a complete sentence.

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isyllus isyllus · Answer 1 · 2020-08-30T03:02:56+02:00

Answer:

Additional 26 pendants are to be sold to make profit.

Step-by-step explanation:

Rent of booth at the craft fair = $200

Cost of material for each pendant = $7.80

Let Kelsey makes [tex]x[/tex] number of pendants.

To calculate the total spending, we have to add the rent of booth at the craft fair and cost of material for [tex]x[/tex] number of pendants.

Cost of material for [tex]x[/tex] number of pendants = Cost of material for each pendant multiplied by number of pendants

Cost of material for [tex]x[/tex] number of pendants = $7.80 [tex]\times[/tex] [tex]x[/tex]

So, total cost = $200 + $7.80 [tex]\times[/tex] [tex]x[/tex]

Now, each pendant is sold at $13.50

So, total money made by selling [tex]x[/tex] pendants = $13.50 [tex]\times[/tex] [tex]x[/tex]

For making profit, total money made must be greater than the total cost.

Therefore, the inequality becomes:

[tex]\bold{13.50 \times x > 200+7.80\times x }[/tex]

Let us solve the inequality now:

[tex]13.50x - 7.80x>200\\\Rightarrow 5.7x > 200\\\Rightarrow \bold{x > 35.08}[/tex]

So, at least 36 pendants are to be sold to make a profit.

Additional 36-10 = 26 pendants are to be sold to make profit.