Question
6 Mia makes three lamps for a total cost of \( \$ 100 \). Mia sells one of the lamps for \( \$ 40 \) and another for \( \$ 35 \). For what price must she sell the third lamp to achieve a profit? more than \( \$ 25 \) less than \( \$ 25 \) 0 exactly 25 a profit is not possible
Ask by Montgomery Schmidt. in Australia
Feb 07,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Mia must sell the third lamp for more than $25 to make a profit.
Solution
Total cost for all three lamps is $100. Mia sold two lamps for $40 and $35, which brings in a total of $75. Let x be the selling price of the third lamp. Then the total sale revenue is:
$75 + x
To make a profit, her total revenue must be greater than her total cost:
$75 + x > $100
Subtract $75 from both sides:
x > $25
Thus, in order to make a profit, she must sell the third lamp for more than $25.
Answer: more than $25
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To determine the selling price needed for the third lamp, let's first calculate the total revenue Mia has from selling the first two lamps. She sells one for \( \$ 40 \) and another for \( \$ 35 \), giving her a total of \( 40 + 35 = \$ 75 \). Since Mia's total cost for producing the lamps was \( \$ 100 \), she needs to at least recover this amount. To achieve a profit, her total revenue must exceed \( \$ 100 \). Therefore, the price for the third lamp, denoted as \( x \), needs to satisfy the equation \( 75 + x > 100 \) or \( x > 25 \). This means she must sell the third lamp for more than \( \$ 25 \) to achieve any profit. Thus, the answer is: more than \( \$ 25 \).
