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

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