samir, a carpenter, spent $300 on specialty tools to make toy horses for children. for each horse he makes…
samir, a carpenter, spent $300 on specialty tools to make toy horses for children. for each horse he makes, he spends $75 on supplies. he charges $125 for each horse. how many horses must samir sell in order to break even?
Answer
Explanation:
Step1: Set up cost - revenue equations
Let $x$ be the number of toy horses. The total cost $C$ is the sum of the cost of tools and the cost of supplies per horse times the number of horses, so $C = 300+75x$. The total revenue $R$ is the selling - price per horse times the number of horses, so $R = 125x$.
Step2: Set cost equal to revenue for break - even
At the break - even point, $C = R$. So we set up the equation $300 + 75x=125x$.
Step3: Solve the equation for $x$
Subtract $75x$ from both sides: $300=125x - 75x$. Simplify the right - hand side to get $300 = 50x$. Then divide both sides by 50: $x=\frac{300}{50}=6$.
Answer:
6