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The soccer team is selling keys chains to raise money for the team. They ordered 100 key chains that cost $0.25 each. There is a flat shipping rate of $8. The team sells the key chains for $2 each. Write an algebraic inequality to find the fewest number of key chains,k, the team must sell to make the profit. What is the fewest number of key chains the team must sell to make a profit? Show your work and explain your thinking.

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MissPhiladelphia
The formula to get the correct answer to question is this:

1.) To get the total cost of goods bought:
((100 key chains) x ($0.25 purchasing cost)) + ($8 shipping rate) = $33
Which means each key chain essentially costs $0.33 each
2.) To get the number of units they should sell to make profit:
Breakeven = Costs/Price meaning $33/$2 = 16.5
They should sell 16.5 units to make a profit.

Answer:

The need to sell 17 key chains to make profits.

Step-by-step explanation:

  • Each key costs $0.25. They oreders 100 key chains.
  • The spent $8 on shipping.
  • They sold the key chaind for $2 each.

According to the given information, the team invested

[tex]0.25(100)=25[/tex], that is, $25 on key chains.

With the shipping, [tex]25+8=33[/tex].

So, the invested 33$. That means they need to sell in order to have an income greater than $33 to make profits, that's the condition.

Therefore, this situation can be modeled as

[tex]2x>33[/tex]

In words, the sell $2 per key chain must obtaine more than $33.

Then, we solve for [tex]x[/tex]

[tex]x>\frac{33}{2}= 16.5[/tex]

So, the need to sell 17 key chains to make profits. Notice, if they sell 16 they would make $32, which is under the condition to make profits.

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