107k views
1 vote
You went to the mall to buy a sweater that was 30% off and you had an additional 20% off coupon. The cashier took the 20% off first and then the 30% off of the reduced amount second. The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second. Would it matter which way this was done? Why or why not?

User Ben Baron
by
9.4k points

1 Answer

5 votes

Step-by-step explanation

let's check every case,

Step 1

A)The cashier took the 20% off first and then the 30% off of the reduced amount second.

let x represents the original price

to find the 20% we can use


\begin{gathered} new\text{ price = original price *\lparen}(100-discount)/(100)) \\ so \\ new\text{ price= x*\lparen}(100-20)/(100)=x*((80)/(100))=0.8x \\ new\text{ price =}0.8c \end{gathered}

then,the 30 % of the reduced amount, so


\begin{gathered} final\text{ price = original price *\lparen}(100-discount)/(100)) \\ so \\ final\text{ price= \lparen0.8x\rparen *\lparen}(100-30)/(100)=(0.8x)*((70)/(100))=(0.8x)(0.7)=0.56x \\ final\text{ price =0.56x} \end{gathered}

Step 2

B)The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second

so

i) 30 of the first


\begin{gathered} new\text{ price = original price *\lparen}(100-discount)/(100)) \\ so \\ new\text{ price= x*\lparen}(100-30)/(100))=x*((70)/(100))=0.7x \\ new\text{ price =}0.7c \end{gathered}

then, 20 % off the reduced amount


\begin{gathered} final\text{ price = original price *\lparen}(100-discount)/(100)) \\ so \\ final\text{ price= \lparen0.7x\rparen *\lparen}(100-20)/(100)=(0.7x)*((80)/(100))=(0.7x)(0.8)=0.56x \\ final\text{ price =0.56x} \end{gathered}

Step 3

so, we can conclude in both cases the final price will be the same, becuase we have a triple product


\begin{gathered} x*0.8*0.7=x*0.7*0.8 \\ 0.56x=0.56x \end{gathered}

so, the answer is

it does not matter which way the calculation is done, because the order does not affect the product

I hope this helps you

User Ved Singh
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories