Question

a music store originally purchased a piano at a cost of $892.03 and marked it up 125%. after a few weeks, however, the store discounted the piano 50% in order to make room for new merchandise. what was the discounted price? $ submit

Explanation:

Step1: Calculate the marked - up price

The formula for calculating the marked - up price is $Marked\ up\ price = Cost\times(1 + Mark\ up\ rate)$. The cost of the piano is $C=\$892.03$ and the mark - up rate is $r = 125\%=1.25$. So the marked - up price $M$ is $M=892.03\times(1 + 1.25)$.
First, calculate $1 + 1.25=2.25$. Then $M = 892.03\times2.25=\$2007.0675$.

Step2: Calculate the discounted price

The formula for calculating the discounted price is $Discounted\ price=Marked\ up\ price\times(1 - Discount\ rate)$. The discount rate is $d = 50\%=0.5$. So the discounted price $D$ is $D = 2007.0675\times(1 - 0.5)$.
First, calculate $1-0.5 = 0.5$. Then $D=2007.0675\times0.5=\$1003.53375\approx\$1003.53$

Answer:

$\$1003.53$ (or $\$1003.53375$ if more precision is needed)