To determine how many rugs Pam needs to sell for her sales to equal her expenses, we first need to create an equation based on her revenue and expenses.
Revenue
Pam sells each rug for $50. If she sells \( r \) rugs, her total revenue is: \[ \text{Revenue} = 50r \]
Expenses
Pam has fixed and variable costs associated with selling the rugs.
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Fixed costs: The initial investment in weaving equipment is $98.
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Variable costs: For each rug, she spends $38.20 on materials and $4.80 on shipping. Therefore, the total cost per rug is: \[ 38.20 + 4.80 = 43 \] Thus, her total variable expenses for \( r \) rugs are: \[ \text{Variable Costs} = 43r \] So, the total expenses (fixed costs + variable costs) are: \[ \text{Total Expenses} = 98 + 43r \]
Setting up the equation
To find the number of rugs Pam must sell so that her sales equal her expenses, we set the revenue equal to the total expenses: \[ 50r = 98 + 43r \]
Solving the equation
Now we will solve this equation for \( r \):
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Subtract \( 43r \) from both sides: \[ 50r - 43r = 98 \] \[ 7r = 98 \]
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Now, divide both sides by 7: \[ r = \frac{98}{7} \] \[ r = 14 \]
Conclusion
Pam must sell 14 rugs for her sales to equal her expenses.