We appreciate your visit to Core Standards Algebra ICheckpoint Problem Solving with Linear Equations and InequalitiesBrennan recently spent tex 160 tex on woodworking tools so he can make and sell. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find out how many mailboxes Brennan must make and sell to cover his initial cost and make a profit, let's break it down step by step.
1. Identify the Costs and Earnings:
- Initial cost for tools: [tex]$160
- Cost to make each mailbox: $[/tex]14
- Selling price of each mailbox: [tex]$40
2. Calculate the Profit per Mailbox:
- Profit earned from each mailbox sold is the selling price minus the cost to make it.
- Profit per mailbox = $[/tex]40 (selling price) - [tex]$14 (cost to make one) = $[/tex]26
3. Set Up the Inequality for Profit:
In order to make a profit, the total profit from selling mailboxes should be greater than the initial cost for tools.
- Let [tex]\( x \)[/tex] represent the number of mailboxes Brennan sells.
- Total profit = Profit per mailbox × Number of mailboxes = [tex]$26 × \( x \)
- For a profit to occur: $[/tex]26x > 160
4. Solve the Inequality:
- [tex]\( x > \frac{160}{26} \)[/tex]
5. Calculate the Minimum Number of Mailboxes:
- [tex]\( x \approx 6.154 \)[/tex]
Brennan must sell at least 7 mailboxes to make a profit, since he cannot sell a fractional part of a mailbox.
From the given choices, the correct inequality is:
- [tex]\( 40x > 160 + 14x \)[/tex]
This choice correctly represents the condition where the revenue from selling [tex]\( x \)[/tex] mailboxes exceeds the sum of the initial cost and the production cost for [tex]\( x \)[/tex] mailboxes.
1. Identify the Costs and Earnings:
- Initial cost for tools: [tex]$160
- Cost to make each mailbox: $[/tex]14
- Selling price of each mailbox: [tex]$40
2. Calculate the Profit per Mailbox:
- Profit earned from each mailbox sold is the selling price minus the cost to make it.
- Profit per mailbox = $[/tex]40 (selling price) - [tex]$14 (cost to make one) = $[/tex]26
3. Set Up the Inequality for Profit:
In order to make a profit, the total profit from selling mailboxes should be greater than the initial cost for tools.
- Let [tex]\( x \)[/tex] represent the number of mailboxes Brennan sells.
- Total profit = Profit per mailbox × Number of mailboxes = [tex]$26 × \( x \)
- For a profit to occur: $[/tex]26x > 160
4. Solve the Inequality:
- [tex]\( x > \frac{160}{26} \)[/tex]
5. Calculate the Minimum Number of Mailboxes:
- [tex]\( x \approx 6.154 \)[/tex]
Brennan must sell at least 7 mailboxes to make a profit, since he cannot sell a fractional part of a mailbox.
From the given choices, the correct inequality is:
- [tex]\( 40x > 160 + 14x \)[/tex]
This choice correctly represents the condition where the revenue from selling [tex]\( x \)[/tex] mailboxes exceeds the sum of the initial cost and the production cost for [tex]\( x \)[/tex] mailboxes.
Thanks for taking the time to read Core Standards Algebra ICheckpoint Problem Solving with Linear Equations and InequalitiesBrennan recently spent tex 160 tex on woodworking tools so he can make and sell. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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