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Pam recently started selling custom T-shirts online. She spent on screen-printing tools, and she spends per shirt on supplies. She is selling each shirt for .Which equation can you use to find , the number of T-shirts Pam must sell for her sales to equal her expenses?Choices:(A) (B) How many T-shirts must Pam sell for her sales to equal her expenses? T-shirts
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Q. Pam recently started selling custom T-shirts online. She spent on screen-printing tools, and she spends per shirt on supplies. She is selling each shirt for .Which equation can you use to find , the number of T-shirts Pam must sell for her sales to equal her expenses?Choices:(A) (B) How many T-shirts must Pam sell for her sales to equal her expenses? T-shirts
- Set Up Equation: To find the break-even point where sales equal expenses, we need to set up an equation where the total cost equals the total revenue.
- Initial Expenses and Costs: Pam's initial expenses are \$\(504\) for screen-printing tools. Her variable cost per shirt is \$\(4\).\(50\), and she sells each shirt for \$\(15\). Let's denote the number of shirts she needs to sell as \(s\).
- Total Cost Calculation: The total cost for ' extit{s}' shirts is the initial cost plus the cost per shirt times the number of shirts, which is \$\(504\) + \$\(4\).\(50\) extit{s}.
- Total Revenue Calculation: The total revenue from selling \(s\) shirts is \(\$15\) times the number of shirts, which is \(\$15s\).
- Equation Simplification: To find the break-even point, we set the total cost equal to the total revenue: \(\$504 + \$4.50s = \$15s\).
- Isolate Variable 's': This equation simplifies to the equation \((B)15s = 504 + 4.5s\), which is the correct equation to use to find the number of T-shirts Pam must sell for her sales to equal her expenses.
- Division to Find 's': Now, we need to solve for 's'. We can do this by subtracting \(\$4.50s\) from both sides of the equation to isolate 's' on one side: \(\$15s - \$4.50s = \$504\).
- Final Answer: Subtracting \(\$4.50s\) from \(\$15s\) gives us \(\$10.50s = \$504\).
- Final Answer: Subtracting \(\$4.50s\) from \(\$15s\) gives us \(\$10.50s = \$504\).To find 's', we divide both sides of the equation by \(\$10.50\): \(\frac{\$10.50s}{\$10.50} = \frac{\$504}{\$10.50}\).
- Final Answer: Subtracting \(\$4.50s\) from \(\$15s\) gives us \(\$10.50s = \$504\). To find 's', we divide both sides of the equation by \(\$10.50\): \(\frac{\$10.50s}{\$10.50} = \frac{\$504}{\$10.50}\). Calculating the division gives us \(s = 48\). Therefore, Pam must sell \(48\) T-shirts to break even.
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