Question

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?

Answer 1

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

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

then,the 30 % of the reduced amount, so

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

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

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

then, 20 % off the reduced amount

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

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