jakes cameras purchased a digital camera at a wholesale cost of $80. they marked up the price 50 percent…
jakes cameras purchased a digital camera at a wholesale cost of $80. they marked up the price 50 percent above the wholesale cost to use as their selling price. after every month that the camera didnt sell, the store reduced the selling price by 25 percent. after how many monthly price reductions did the price dip below the wholesale cost?\no after 2 monthly price reductions\no after 3 monthly price reductions\no after 4 monthly price reductions\no after 5 monthly price reductions
Answer
Explanation:
Step1: Calculate the initial selling price
The wholesale cost is $80. The markup is 50% of $80. The initial selling price $P_0$ is $80\times(1 + 50%)=80\times1.5 = 120$.
Step2: Set up the formula for the price after $n$ reductions
After each reduction of 25%, the new price is 75% (or 0.75) of the previous - price. So the price $P_n$ after $n$ monthly price - reductions is $P_n=120\times(0.75)^n$.
Step3: Find $n$ when $P_n<80$
We want to find $n$ such that $120\times(0.75)^n<80$. Rearrange the inequality to get $(0.75)^n<\frac{80}{120}=\frac{2}{3}\approx0.667$. When $n = 2$: $(0.75)^2=0.75\times0.75 = 0.5625$, and $120\times0.5625 = 67.5<80$.
Answer:
after 2 monthly price reductions