alisha must wear dress pants and a blouse to work every day. she can buy an all - cotton blouse for $35, but…

alisha must wear dress pants and a blouse to work every day. she can buy an all - cotton blouse for $35, but it needs to be sent to the dry cleaner to be washed and ironed for $5 after each use. she can buy a wash - and - wear blouse of the same quality for $50, which she can stick in her washing machine and hang up to dry. if we ignore the cost of using her washing machine (which is offset by the cost of driving to the dry cleaner), after how many cleanings will she break even on buying the more expensive blouse?\na. 10\nb. 7\nc. 3\nd. 25

alisha must wear dress pants and a blouse to work every day. she can buy an all - cotton blouse for $35, but it needs to be sent to the dry cleaner to be washed and ironed for $5 after each use. she can buy a wash - and - wear blouse of the same quality for $50, which she can stick in her washing machine and hang up to dry. if we ignore the cost of using her washing machine (which is offset by the cost of driving to the dry cleaner), after how many cleanings will she break even on buying the more expensive blouse?\na. 10\nb. 7\nc. 3\nd. 25

Answer

Explanation:

Step1: Set up cost - equations

Let $n$ be the number of cleanings. The cost of the all - cotton blouse $C_1$ is the initial cost plus the cost of dry - cleaning per use times the number of uses. So $C_1 = 35+5n$. The cost of the wash - and - wear blouse $C_2$ is its initial cost, $C_2 = 50$.

Step2: Set $C_1 = C_2$ and solve for $n$

We set up the equation $35 + 5n=50$. Subtract 35 from both sides: $5n=50 - 35$, so $5n = 15$. Then divide both sides by 5: $n=\frac{15}{5}=3$.

Answer:

C. 3