Question

ProblemPrintA local store has a sale rack for clearance merchandise. The sign on the rack says,"Marked down an additional 20% each day!"Sten has been thinking about buying a jacket that costs $100. The clerk tells him it willbe moved to the sale rack tomorrow. Sten is happy about this and decides he'll goback to the store in five days when the jacket will be freeWhen he gets to the store five days later, he sees that the jacket is not actually free.What price is really marked on the jacket?ExtraExtra: Why did Sten think it would be free? How would you explain to Sten why his reasoning iswrong?

Answer 1

The marked price is $100 and price down is 20% each day.

The marked down is given on the price of jacket on that day. For example,

Determine the price of jacket after one day.

`\begin{gathered} P_1=100-(20)/(100)\cdot100 \\ =100-20 \\ =80 \end{gathered}`

So on first day discount is $20.

On second day 20% price down of $80 not $100.

Determine the price of jacket on second day.

`\begin{gathered} P_2=80-(20)/(100)\cdot80 \\ =80-16 \\ =64 \end{gathered}`

So on second day discount is only $16 not $20 as on first day.

Determine the price of jacket on third day.

`\begin{gathered} P_3=64-(20)/(100)\cdot64 \\ =64-12.8 \\ =51.2 \end{gathered}`

The price of jacket on third day is $51.2.

Determine the price of jacket on fourth day.

`\begin{gathered} P_4=51.2-(20)/(100)\cdot51.2 \\ =51.2-10.24 \\ =40.96 \end{gathered}`

The price of jacket on fourth day is $40.96.

Determine the price of jacket on fifth day.

`\begin{gathered} P_5=40.96-(20)/(100)\cdot40.96 \\ =40.96-8.192 \\ =32.768 \end{gathered}`

So after 5 day price marked on the jacket is $32.768.

The Sten is wrong as he think that 20% per day marked price down means in 5 days the discount is,

`5*20=100`

and 100% discount means jacket is free.

But in actual the discount is provided on per day marked price not on $100. On first day discount is on $100 as cost of jacket is $100 but on second day cost of jacket decrease to $80. So price is down by 20% of 80 not by 20% of 100. So after 5 days cost of Jacket is $32.768 not $0.

Answer: Cost of jacket after 5 days is $32.768.