27. the tie shop sells its ties for $41 each. the shop has weekly fixed costs of $845, and each tie costs…
27. the tie shop sells its ties for $41 each. the shop has weekly fixed costs of $845, and each tie costs $22. how many ties must be sold to make a profit?
Answer
Explanation:
Step1: Define profit formula
Profit = Revenue - Cost. Let $x$ be the number of ties sold. Revenue $R = 41x$, and cost $C=845 + 22x$. To make a profit, $R>C$, so $41x>845 + 22x$.
Step2: Solve the inequality
Subtract $22x$ from both sides: $41x-22x>845+22x - 22x$, which simplifies to $19x>845$.
Step3: Find the value of $x$
Divide both sides by 19: $x>\frac{845}{19}$. Calculate $\frac{845}{19}\approx44.47$. Since the number of ties must be a whole - number, $x = 45$.
Answer:
45